Daily Papers

Chain-of-thought reasoning in large language models often creates an "overthinking trap," leading to excessive computational cost and latency for unreliable accuracy gains. Prior work has typically relied on global, static controls that risk penalizing necessary reasoning. We introduce a sample-level, soft reinforcement learning compression method that penalizes inefficiently long rollouts, but only on problems where the model has already mastered and already produced a more concise rollout. Our experiments show that this method reduces average response length by 20-40% with comparable or higher accuracy. Crucially, the compression exhibits strong cross-domain generalization; a model trained on math spontaneously shortens responses on unseen tasks like code, instruction following, and general knowledge QA, with stable or improved accuracy. We demonstrate a stable post-training curriculum (accuracy-compression-accuracy) that can ultimately produce models that are more accurate and reason more concisely, arguing that such compression method should be a standard phase in developing efficient reasoning models.

Numerous capability and safety techniques of Large Language Models (LLMs), including RLHF, automated red-teaming, prompt engineering, and infilling, can be cast as sampling from an unnormalized target distribution defined by a given reward or potential function over the full sequence. In this work, we leverage the rich toolkit of Sequential Monte Carlo (SMC) for these probabilistic inference problems. In particular, we use learned twist functions to estimate the expected future value of the potential at each timestep, which enables us to focus inference-time computation on promising partial sequences. We propose a novel contrastive method for learning the twist functions, and establish connections with the rich literature of soft reinforcement learning. As a complementary application of our twisted SMC framework, we present methods for evaluating the accuracy of language model inference techniques using novel bidirectional SMC bounds on the log partition function. These bounds can be used to estimate the KL divergence between the inference and target distributions in both directions. We apply our inference evaluation techniques to show that twisted SMC is effective for sampling undesirable outputs from a pretrained model (a useful component of harmlessness training and automated red-teaming), generating reviews with varied sentiment, and performing infilling tasks.

Active Visual Exploration (AVE) is a task that involves dynamically selecting observations (glimpses), which is critical to facilitate comprehension and navigation within an environment. While modern AVE methods have demonstrated impressive performance, they are constrained to fixed-scale glimpses from rigid grids. In contrast, existing mobile platforms equipped with optical zoom capabilities can capture glimpses of arbitrary positions and scales. To address this gap between software and hardware capabilities, we introduce AdaGlimpse. It uses Soft Actor-Critic, a reinforcement learning algorithm tailored for exploration tasks, to select glimpses of arbitrary position and scale. This approach enables our model to rapidly establish a general awareness of the environment before zooming in for detailed analysis. Experimental results demonstrate that AdaGlimpse surpasses previous methods across various visual tasks while maintaining greater applicability in realistic AVE scenarios.

We study the conformal bootstrap of 1D CFTs on the straight Maldacena-Wilson line in 4D {cal N}=4 super-Yang-Mills theory. We introduce an improved truncation scheme with an 'OPE tail' approximation and use it to reproduce the 'bootstrability' results of Cavagli\`a et al. for the OPE-coefficients squared of the first three unprotected operators. For example, for the first OPE-coefficient squared at 't Hooft coupling (4pi)^2, linear-functional methods with two sum rules from integrated correlators give the rigorous result 0.294014873 pm 4.88 cdot 10^{-8}, whereas our methods give with machine-precision computations 0.294014228 pm 6.77 cdot 10^{-7}. For our numerical searches, we benchmark the Reinforcement Learning Soft Actor-Critic algorithm against an Interior Point Method algorithm (IPOPT) and comment on the merits of each algorithm.

In reinforcement learning (RL), function approximation errors are known to easily lead to the Q-value overestimations, thus greatly reducing policy performance. This paper presents a distributional soft actor-critic (DSAC) algorithm, which is an off-policy RL method for continuous control setting, to improve the policy performance by mitigating Q-value overestimations. We first discover in theory that learning a distribution function of state-action returns can effectively mitigate Q-value overestimations because it is capable of adaptively adjusting the update stepsize of the Q-value function. Then, a distributional soft policy iteration (DSPI) framework is developed by embedding the return distribution function into maximum entropy RL. Finally, we present a deep off-policy actor-critic variant of DSPI, called DSAC, which directly learns a continuous return distribution by keeping the variance of the state-action returns within a reasonable range to address exploding and vanishing gradient problems. We evaluate DSAC on the suite of MuJoCo continuous control tasks, achieving the state-of-the-art performance.

Extensive efforts have been made to improve the generalization ability of Reinforcement Learning (RL) methods via domain randomization and data augmentation. However, as more factors of variation are introduced during training, optimization becomes increasingly challenging, and empirically may result in lower sample efficiency and unstable training. Instead of learning policies directly from augmented data, we propose SOft Data Augmentation (SODA), a method that decouples augmentation from policy learning. Specifically, SODA imposes a soft constraint on the encoder that aims to maximize the mutual information between latent representations of augmented and non-augmented data, while the RL optimization process uses strictly non-augmented data. Empirical evaluations are performed on diverse tasks from DeepMind Control suite as well as a robotic manipulation task, and we find SODA to significantly advance sample efficiency, generalization, and stability in training over state-of-the-art vision-based RL methods.

Deep reinforcement learning (RL) has achieved significant success, yet its application in real-world scenarios is often hindered by a lack of robustness to environmental uncertainties. To solve this challenge, some robust RL algorithms have been proposed, but most are limited to tabular settings. In this work, we propose Distributionally Robust Soft Actor-Critic (DR-SAC), a novel algorithm designed to enhance the robustness of the state-of-the-art Soft Actor-Critic (SAC) algorithm. DR-SAC aims to maximize the expected value with entropy against the worst possible transition model lying in an uncertainty set. A distributionally robust version of the soft policy iteration is derived with a convergence guarantee. For settings where nominal distributions are unknown, such as offline RL, a generative modeling approach is proposed to estimate the required nominal distributions from data. Furthermore, experimental results on a range of continuous control benchmark tasks demonstrate our algorithm achieves up to 9.8 times the average reward of the SAC baseline under common perturbations. Additionally, compared with existing robust reinforcement learning algorithms, DR-SAC significantly improves computing efficiency and applicability to large-scale problems.

Model-free deep reinforcement learning (RL) algorithms have been demonstrated on a range of challenging decision making and control tasks. However, these methods typically suffer from two major challenges: very high sample complexity and brittle convergence properties, which necessitate meticulous hyperparameter tuning. Both of these challenges severely limit the applicability of such methods to complex, real-world domains. In this paper, we propose soft actor-critic, an off-policy actor-critic deep RL algorithm based on the maximum entropy reinforcement learning framework. In this framework, the actor aims to maximize expected reward while also maximizing entropy. That is, to succeed at the task while acting as randomly as possible. Prior deep RL methods based on this framework have been formulated as Q-learning methods. By combining off-policy updates with a stable stochastic actor-critic formulation, our method achieves state-of-the-art performance on a range of continuous control benchmark tasks, outperforming prior on-policy and off-policy methods. Furthermore, we demonstrate that, in contrast to other off-policy algorithms, our approach is very stable, achieving very similar performance across different random seeds.

The soft-thinking paradigm for Large Language Model (LLM) reasoning can outperform the conventional discrete-token Chain-of-Thought (CoT) reasoning in some scenarios, underscoring its research and application value. However, while the discrete-token CoT reasoning pattern can be reinforced through policy optimization algorithms such as group relative policy optimization (GRPO), extending the soft-thinking pattern with Reinforcement Learning (RL) remains challenging. This difficulty stems from the complexities of injecting stochasticity into soft-thinking tokens and updating soft-thinking policies accordingly. As a result, previous attempts to combine soft-thinking with GRPO typically underperform their discrete-token GRPO counterparts. To fully unlock the potential of soft-thinking, this paper presents a novel policy optimization algorithm, SofT-GRPO, to reinforce LLMs under the soft-thinking reasoning pattern. SofT-GRPO injects the Gumbel noise into logits, employs the Gumbel-Softmax technique to avoid soft-thinking tokens outside the pre-trained embedding space, and leverages the reparameterization trick in policy gradient. We conduct experiments across base LLMs ranging from 1.5B to 7B parameters, and results demonstrate that SofT-GRPO enables soft-thinking LLMs to slightly outperform discrete-token GRPO on Pass@1 (+0.13% on average accuracy), while exhibiting a substantial uplift on Pass@32 (+2.19% on average accuracy). Codes and weights are available on https://github.com/zz1358m/SofT-GRPO-master

Long context reasoning in large language models (LLMs) has demonstrated enhancement of their cognitive capabilities via chain-of-thought (CoT) inference. Training such models is usually done via reinforcement learning with verifiable rewards (RLVR) in reasoning based problems, like math and programming. However, RLVR is limited by several bottlenecks, such as, lack of dense reward, and inadequate sample efficiency. As a result, it requires significant compute resources in post-training phase. To overcome these limitations, in this work, we propose Semantic Soft Bootstrapping (SSB), a self-distillation technique, in which the same base language model plays the role of both teacher and student, but receives different semantic contexts about the correctness of its outcome at training time. The model is first prompted with a math problem and several rollouts are generated. From them, the correct and most common incorrect response are filtered, and then provided to the model in context to produce a more robust, step-by-step explanation with a verified final answer. This pipeline automatically curates a paired teacher-student training set from raw problem-answer data, without any human intervention. This generation process also produces a sequence of logits, which is what the student model tries to match in the training phase just from the bare question alone. In our experiment, Qwen2.5-3B-Instruct on GSM8K dataset via parameter-efficient fine-tuning. We then tested its accuracy on MATH500, and AIME2024 benchmarks. Our experiments show a jump of 10.6%, and 10% improvements in accuracy, respectively, over group relative policy optimization (GRPO), which is a commonly used RLVR algorithm. Our code is available at https://github.com/purbeshmitra/semantic-soft-bootstrapping, and the model, curated dataset is available at https://huggingface.co/purbeshmitra/semantic-soft-bootstrapping.

Large language model post-training relies on reinforcement learning to improve model capability and alignment quality. However, the off-policy training paradigm introduces distribution shift, which often pushes the policy beyond the trust region, leading to training instabilities manifested as fluctuations in policy entropy and unstable gradients. Although PPO-Clip mitigates this issue through importance clipping, it still overlooks the global distributional shift of actions. To address these challenges, we propose using the entropy ratio between the current and previous policies as a new global metric that effectively quantifies the relative change in policy exploration throughout updates. Building on this metric, we introduce an Entropy Ratio Clipping (ERC) mechanism that imposes bidirectional constraints on the entropy ratio. This stabilizes policy updates at the global distribution level and compensates for the inability of PPO-clip to regulate probability shifts of un-sampled actions. We integrate ERC into both DAPO and GPPO reinforcement learning algorithms. Experiments across multiple benchmarks show that ERC consistently improves performance.

Growth in the penetration of renewable energy sources makes supply more uncertain and leads to an increase in the system imbalance. This trend, together with the single imbalance pricing, opens an opportunity for balance responsible parties (BRPs) to perform energy arbitrage in the imbalance settlement mechanism. To this end, we propose a battery control framework based on distributional reinforcement learning (DRL). Our proposed control framework takes a risk-sensitive perspective, allowing BRPs to adjust their risk preferences: we aim to optimize a weighted sum of the arbitrage profit and a risk measure while constraining the daily number of cycles for the battery. We assess the performance of our proposed control framework using the Belgian imbalance prices of 2022 and compare two state-of-the-art RL methods, deep Q learning and soft actor-critic. Results reveal that the distributional soft actor-critic method can outperform other methods. Moreover, we note that our fully risk-averse agent appropriately learns to hedge against the risk related to the unknown imbalance price by (dis)charging the battery only when the agent is more certain about the price.

Existing Maximum-Entropy (MaxEnt) Reinforcement Learning (RL) methods for continuous action spaces are typically formulated based on actor-critic frameworks and optimized through alternating steps of policy evaluation and policy improvement. In the policy evaluation steps, the critic is updated to capture the soft Q-function. In the policy improvement steps, the actor is adjusted in accordance with the updated soft Q-function. In this paper, we introduce a new MaxEnt RL framework modeled using Energy-Based Normalizing Flows (EBFlow). This framework integrates the policy evaluation steps and the policy improvement steps, resulting in a single objective training process. Our method enables the calculation of the soft value function used in the policy evaluation target without Monte Carlo approximation. Moreover, this design supports the modeling of multi-modal action distributions while facilitating efficient action sampling. To evaluate the performance of our method, we conducted experiments on the MuJoCo benchmark suite and a number of high-dimensional robotic tasks simulated by Omniverse Isaac Gym. The evaluation results demonstrate that our method achieves superior performance compared to widely-adopted representative baselines.

Robot co-design, where the morphology of a robot is optimized jointly with a learned policy to solve a specific task, is an emerging area of research. It holds particular promise for soft robots, which are amenable to novel manufacturing techniques that can realize learned morphologies and actuators. Inspired by nature and recent novel robot designs, we propose to go a step further and explore the novel reconfigurable robots, defined as robots that can change their morphology within their lifetime. We formalize control of reconfigurable soft robots as a high-dimensional reinforcement learning (RL) problem. We unify morphology change, locomotion, and environment interaction in the same action space, and introduce an appropriate, coarse-to-fine curriculum that enables us to discover policies that accomplish fine-grained control of the resulting robots. We also introduce DittoGym, a comprehensive RL benchmark for reconfigurable soft robots that require fine-grained morphology changes to accomplish the tasks. Finally, we evaluate our proposed coarse-to-fine algorithm on DittoGym and demonstrate robots that learn to change their morphology several times within a sequence, uniquely enabled by our RL algorithm. More results are available at https://dittogym.github.io.

Safe offline RL is a promising way to bypass risky online interactions towards safe policy learning. Most existing methods only enforce soft constraints, i.e., constraining safety violations in expectation below thresholds predetermined. This can lead to potentially unsafe outcomes, thus unacceptable in safety-critical scenarios. An alternative is to enforce the hard constraint of zero violation. However, this can be challenging in offline setting, as it needs to strike the right balance among three highly intricate and correlated aspects: safety constraint satisfaction, reward maximization, and behavior regularization imposed by offline datasets. Interestingly, we discover that via reachability analysis of safe-control theory, the hard safety constraint can be equivalently translated to identifying the largest feasible region given the offline dataset. This seamlessly converts the original trilogy problem to a feasibility-dependent objective, i.e., maximizing reward value within the feasible region while minimizing safety risks in the infeasible region. Inspired by these, we propose FISOR (FeasIbility-guided Safe Offline RL), which allows safety constraint adherence, reward maximization, and offline policy learning to be realized via three decoupled processes, while offering strong safety performance and stability. In FISOR, the optimal policy for the translated optimization problem can be derived in a special form of weighted behavior cloning. Thus, we propose a novel energy-guided diffusion model that does not require training a complicated time-dependent classifier to extract the policy, greatly simplifying the training. We compare FISOR against baselines on DSRL benchmark for safe offline RL. Evaluation results show that FISOR is the only method that can guarantee safety satisfaction in all tasks, while achieving top returns in most tasks.

Scaling up the model size and computation has brought consistent performance improvements in supervised learning. However, this lesson often fails to apply to reinforcement learning (RL) because training the model on non-stationary data easily leads to overfitting and unstable optimization. In response, we introduce SimbaV2, a novel RL architecture designed to stabilize optimization by (i) constraining the growth of weight and feature norm by hyperspherical normalization; and (ii) using a distributional value estimation with reward scaling to maintain stable gradients under varying reward magnitudes. Using the soft actor-critic as a base algorithm, SimbaV2 scales up effectively with larger models and greater compute, achieving state-of-the-art performance on 57 continuous control tasks across 4 domains. The code is available at https://dojeon-ai.github.io/SimbaV2.

Reinforcement learning (RL) for continuous control often requires large amounts of online interaction data. Value-based RL methods can mitigate this burden by offering relatively high sample efficiency. Some studies further enhance sample efficiency by incorporating offline demonstration data to "kick-start" training, achieving promising results in continuous control. However, they typically compute the Q-function independently for each action dimension, neglecting interdependencies and making it harder to identify optimal actions when learning from suboptimal data, such as non-expert demonstration and online-collected data during the training process. To address these issues, we propose Auto-Regressive Soft Q-learning (ARSQ), a value-based RL algorithm that models Q-values in a coarse-to-fine, auto-regressive manner. First, ARSQ decomposes the continuous action space into discrete spaces in a coarse-to-fine hierarchy, enhancing sample efficiency for fine-grained continuous control tasks. Next, it auto-regressively predicts dimensional action advantages within each decision step, enabling more effective decision-making in continuous control tasks. We evaluate ARSQ on two continuous control benchmarks, RLBench and D4RL, integrating demonstration data into online training. On D4RL, which includes non-expert demonstrations, ARSQ achieves an average 1.62times performance improvement over SOTA value-based baseline. On RLBench, which incorporates expert demonstrations, ARSQ surpasses various baselines, demonstrating its effectiveness in learning from suboptimal online-collected data. Project page is at https://sites.google.com/view/ar-soft-q

In risk-averse reinforcement learning (RL), the goal is to optimize some risk measure of the returns. A risk measure often focuses on the worst returns out of the agent's experience. As a result, standard methods for risk-averse RL often ignore high-return strategies. We prove that under certain conditions this inevitably leads to a local-optimum barrier, and propose a soft risk mechanism to bypass it. We also devise a novel Cross Entropy module for risk sampling, which (1) preserves risk aversion despite the soft risk; (2) independently improves sample efficiency. By separating the risk aversion of the sampler and the optimizer, we can sample episodes with poor conditions, yet optimize with respect to successful strategies. We combine these two concepts in CeSoR - Cross-entropy Soft-Risk optimization algorithm - which can be applied on top of any risk-averse policy gradient (PG) method. We demonstrate improved risk aversion in maze navigation, autonomous driving, and resource allocation benchmarks, including in scenarios where standard risk-averse PG completely fails.

We introduce the use of reinforcement-learning (RL) techniques to the conformal-bootstrap programme. We demonstrate that suitable soft Actor-Critic RL algorithms can perform efficient, relatively cheap high-dimensional searches in the space of scaling dimensions and OPE-squared coefficients that produce sensible results for tens of CFT data from a single crossing equation. In this paper we test this approach in well-known 2D CFTs, with particular focus on the Ising and tri-critical Ising models and the free compactified boson CFT. We present results of as high as 36-dimensional searches, whose sole input is the expected number of operators per spin in a truncation of the conformal-block decomposition of the crossing equations. Our study of 2D CFTs uses only the global so(2,2) part of the conformal algebra, and our methods are equally applicable to higher-dimensional CFTs. When combined with other, already available, numerical and analytical methods, we expect our approach to yield an exciting new window into the non-perturbative structure of arbitrary (unitary or non-unitary) CFTs.

Improving the multi-step reasoning ability of large language models (LLMs) with offline reinforcement learning (RL) is essential for quickly adapting them to complex tasks. While Direct Preference Optimization (DPO) has shown promise in aligning LLMs with human preferences, it is less suitable for multi-step reasoning tasks because (1) DPO relies on paired preference data, which is not readily available for multi-step reasoning tasks, and (2) it treats all tokens uniformly, making it ineffective for credit assignment in multi-step reasoning tasks, which often come with sparse reward. In this work, we propose OREO (Offline Reasoning Optimization), an offline RL method for enhancing LLM multi-step reasoning. Building on insights from previous works of maximum entropy reinforcement learning, it jointly learns a policy model and value function by optimizing the soft Bellman Equation. We show in principle that it reduces the need to collect pairwise data and enables better credit assignment. Empirically, OREO surpasses existing offline learning methods on multi-step reasoning benchmarks, including mathematical reasoning tasks (GSM8K, MATH) and embodied agent control (ALFWorld). The approach can be extended to a multi-iteration framework when additional resources are available. Furthermore, the learned value function can be leveraged to guide the tree search for free, which can further boost performance during test time.

The tension between data privacy and model utility has become the defining bottleneck for the practical deployment of large language models (LLMs) trained on sensitive corpora including healthcare. Differentially private stochastic gradient descent (DP-SGD) guarantees formal privacy, yet it does so at a pronounced cost: gradients are forcibly clipped and perturbed with noise, degrading sample efficiency and final accuracy. Numerous variants have been proposed to soften this trade-off, but they all share a handicap: their control knobs are hard-coded, global, and oblivious to the evolving optimization landscape. Consequently, practitioners are forced either to over-spend privacy budget in pursuit of utility, or to accept mediocre models in order to stay within privacy constraints. We present RLDP, the first framework to cast DP optimization itself as a closed-loop control problem amenable to modern deep reinforcement learning (RL). RLDP continuously senses rich statistics of the learning dynamics and acts by selecting fine-grained per parameter gradient-clipping thresholds as well as the magnitude of injected Gaussian noise. A soft actor-critic (SAC) hyper-policy is trained online during language model fine-tuning; it learns, from scratch, how to allocate the privacy budget where it matters and when it matters. Across more than 1,600 ablation experiments on GPT2-small, Llama-1B, Llama-3B, and Mistral-7B, RLDP delivers perplexity reductions of 1.3-30.5% (mean 5.4%) and an average 5.6% downstream utility gain. RLDP reaches each baseline's final utility after only 13-43% of the gradient-update budget (mean speed-up 71%), all while honoring the same (epsilon, delta)-DP contract and exhibiting equal or lower susceptibility to membership-inference and canary-extraction attacks.

Learning from Demonstration (LfD) aims to facilitate rapid Reinforcement Learning (RL) by leveraging expert demonstrations to pre-train the RL agent. However, the limited availability of expert demonstration data often hinders its ability to effectively aid downstream RL learning. To address this problem, we propose a novel two-stage method dubbed as Skill-enhanced Reinforcement Learning Acceleration (SeRLA). SeRLA introduces a skill-level adversarial Positive-Unlabeled (PU) learning model to extract useful skill prior knowledge by enabling learning from both limited expert data and general low-cost demonstration data in the offline prior learning stage. Subsequently, it deploys a skill-based soft actor-critic algorithm to leverage this acquired prior knowledge in the downstream online RL stage for efficient training of a skill policy network. Moreover, we develop a simple skill-level data enhancement technique to further alleviate data sparsity and improve both skill prior learning and downstream skill policy training. Our experimental results on multiple standard RL environments show the proposed SeRLA method achieves state-of-the-art performance on accelerating reinforcement learning on downstream tasks, especially in the early learning phase.

Multi-agent reinforcement learning (MARL) has been shown effective for cooperative games in recent years. However, existing state-of-the-art methods face challenges related to sample complexity, training instability, and the risk of converging to a suboptimal Nash Equilibrium. In this paper, we propose a unified framework for learning stochastic policies to resolve these issues. We embed cooperative MARL problems into probabilistic graphical models, from which we derive the maximum entropy (MaxEnt) objective for MARL. Based on the MaxEnt framework, we propose Heterogeneous-Agent Soft Actor-Critic (HASAC) algorithm. Theoretically, we prove the monotonic improvement and convergence to quantal response equilibrium (QRE) properties of HASAC. Furthermore, we generalize a unified template for MaxEnt algorithmic design named Maximum Entropy Heterogeneous-Agent Mirror Learning (MEHAML), which provides any induced method with the same guarantees as HASAC. We evaluate HASAC on six benchmarks: Bi-DexHands, Multi-Agent MuJoCo, StarCraft Multi-Agent Challenge, Google Research Football, Multi-Agent Particle Environment, and Light Aircraft Game. Results show that HASAC consistently outperforms strong baselines, exhibiting better sample efficiency, robustness, and sufficient exploration.

Reinforcement learning has proven its effectiveness in enhancing the reasoning capabilities of large language models. Recent research efforts have progressively extended this paradigm to multimodal reasoning tasks. Due to the inherent complexity and diversity of multimodal tasks, especially in semantic content and problem formulations, existing models often exhibit unstable performance across various domains and difficulty levels. To address these limitations, we propose VL-Cogito, an advanced multimodal reasoning model trained via a novel multi-stage Progressive Curriculum Reinforcement Learning (PCuRL) framework. PCuRL systematically guides the model through tasks of gradually increasing difficulty, substantially improving its reasoning abilities across diverse multimodal contexts. The framework introduces two key innovations: (1) an online difficulty soft weighting mechanism, dynamically adjusting training difficulty across successive RL training stages; and (2) a dynamic length reward mechanism, which encourages the model to adaptively regulate its reasoning path length according to task complexity, thus balancing reasoning efficiency with correctness. Experimental evaluations demonstrate that VL-Cogito consistently matches or surpasses existing reasoning-oriented models across mainstream multimodal benchmarks spanning mathematics, science, logic, and general understanding, validating the effectiveness of our approach.

Deep reinforcement learning (DRL) has emerged as a promising solution to mastering explosive and versatile quadrupedal jumping skills. However, current DRL-based frameworks usually rely on pre-existing reference trajectories obtained by capturing animal motions or transferring experience from existing controllers. This work aims to prove that learning dynamic jumping is possible without relying on imitating a reference trajectory by leveraging a curriculum design. Starting from a vertical in-place jump, we generalize the learned policy to forward and diagonal jumps and, finally, we learn to jump across obstacles. Conditioned on the desired landing location, orientation, and obstacle dimensions, the proposed approach yields a wide range of omnidirectional jumping motions in real-world experiments. Particularly we achieve a 90cm forward jump, exceeding all previous records for similar robots reported in the existing literature. Additionally, the robot can reliably execute continuous jumping on soft grassy grounds, which is especially remarkable as such conditions were not included in the training stage. A supplementary video can be found on: https://www.youtube.com/watch?v=nRaMCrwU5X8. The code associated with this work can be found on: https://github.com/Vassil17/Curriculum-Quadruped-Jumping-DRL.

Microprocessor architects are increasingly resorting to domain-specific customization in the quest for high-performance and energy-efficiency. As the systems grow in complexity, fine-tuning architectural parameters across multiple sub-systems (e.g., datapath, memory blocks in different hierarchies, interconnects, compiler optimization, etc.) quickly results in a combinatorial explosion of design space. This makes domain-specific customization an extremely challenging task. Prior work explores using reinforcement learning (RL) and other optimization methods to automatically explore the large design space. However, these methods have traditionally relied on single-agent RL/ML formulations. It is unclear how scalable single-agent formulations are as we increase the complexity of the design space (e.g., full stack System-on-Chip design). Therefore, we propose an alternative formulation that leverages Multi-Agent RL (MARL) to tackle this problem. The key idea behind using MARL is an observation that parameters across different sub-systems are more or less independent, thus allowing a decentralized role assigned to each agent. We test this hypothesis by designing domain-specific DRAM memory controller for several workload traces. Our evaluation shows that the MARL formulation consistently outperforms single-agent RL baselines such as Proximal Policy Optimization and Soft Actor-Critic over different target objectives such as low power and latency. To this end, this work opens the pathway for new and promising research in MARL solutions for hardware architecture search.

Nitrogen (N) management is critical to sustain soil fertility and crop production while minimizing the negative environmental impact, but is challenging to optimize. This paper proposes an intelligent N management system using deep reinforcement learning (RL) and crop simulations with Decision Support System for Agrotechnology Transfer (DSSAT). We first formulate the N management problem as an RL problem. We then train management policies with deep Q-network and soft actor-critic algorithms, and the Gym-DSSAT interface that allows for daily interactions between the simulated crop environment and RL agents. According to the experiments on the maize crop in both Iowa and Florida in the US, our RL-trained policies outperform previous empirical methods by achieving higher or similar yield while using less fertilizers

We propose a simple data augmentation technique that can be applied to standard model-free reinforcement learning algorithms, enabling robust learning directly from pixels without the need for auxiliary losses or pre-training. The approach leverages input perturbations commonly used in computer vision tasks to regularize the value function. Existing model-free approaches, such as Soft Actor-Critic (SAC), are not able to train deep networks effectively from image pixels. However, the addition of our augmentation method dramatically improves SAC's performance, enabling it to reach state-of-the-art performance on the DeepMind control suite, surpassing model-based (Dreamer, PlaNet, and SLAC) methods and recently proposed contrastive learning (CURL). Our approach can be combined with any model-free reinforcement learning algorithm, requiring only minor modifications. An implementation can be found at https://sites.google.com/view/data-regularized-q.

The majority of language model training builds on imitation learning. It covers pretraining, supervised fine-tuning, and affects the starting conditions for reinforcement learning from human feedback (RLHF). The simplicity and scalability of maximum likelihood estimation (MLE) for next token prediction led to its role as predominant paradigm. However, the broader field of imitation learning can more effectively utilize the sequential structure underlying autoregressive generation. We focus on investigating the inverse reinforcement learning (IRL) perspective to imitation, extracting rewards and directly optimizing sequences instead of individual token likelihoods and evaluate its benefits for fine-tuning large language models. We provide a new angle, reformulating inverse soft-Q-learning as a temporal difference regularized extension of MLE. This creates a principled connection between MLE and IRL and allows trading off added complexity with increased performance and diversity of generations in the supervised fine-tuning (SFT) setting. We find clear advantages for IRL-based imitation, in particular for retaining diversity while maximizing task performance, rendering IRL a strong alternative on fixed SFT datasets even without online data generation. Our analysis of IRL-extracted reward functions further indicates benefits for more robust reward functions via tighter integration of supervised and preference-based LLM post-training.

Prompting has shown impressive success in enabling large pretrained language models (LMs) to perform diverse NLP tasks, especially when only few downstream data are available. Automatically finding the optimal prompt for each task, however, is challenging. Most existing work resorts to tuning soft prompt (e.g., embeddings) which falls short of interpretability, reusability across LMs, and applicability when gradients are not accessible. Discrete prompt, on the other hand, is difficult to optimize, and is often created by "enumeration (e.g., paraphrasing)-then-selection" heuristics that do not explore the prompt space systematically. This paper proposes RLPrompt, an efficient discrete prompt optimization approach with reinforcement learning (RL). RLPrompt formulates a parameter-efficient policy network that generates the desired discrete prompt after training with reward. To overcome the complexity and stochasticity of reward signals by the large LM environment, we incorporate effective reward stabilization that substantially enhances the training efficiency. RLPrompt is flexibly applicable to different types of LMs, such as masked (e.g., BERT) and left-to-right models (e.g., GPTs), for both classification and generation tasks. Experiments on few-shot classification and unsupervised text style transfer show superior performance over a wide range of existing finetuning or prompting methods. Interestingly, the resulting optimized prompts are often ungrammatical gibberish text; and surprisingly, those gibberish prompts are transferrable between different LMs to retain significant performance, indicating LM prompting may not follow human language patterns.

Mobile edge computing (MEC) is essential for next-generation mobile network applications that prioritize various performance metrics, including delays and energy efficiency. However, conventional single-objective scheduling solutions cannot be directly applied to practical systems in which the preferences (i.e., the weights of different objectives) are often unknown or challenging to specify in advance. In this study, we formulate a multi-objective offloading problem for MEC with multiple edges to minimize the sum of expected long-term energy consumption and delay while considering unknown preferences. To address the challenge of unknown preferences and the potentially diverse MEC systems, we propose a generalizable multi-objective (deep) reinforcement learning (GMORL)-based tasks offloading framework, which employs the Discrete Soft Actor-Critic (Discrete-SAC) method. Our method uses a single policy model to efficiently schedule tasks based on varying preferences and adapt to heterogeneous MEC systems with different CPU frequencies and server quantities. Under the proposed framework, we introduce a histogram-based state encoding method for constructing features for multiple edges in MEC systems, a sophisticated reward function for accurately computing the utilities of delay and energy consumption, and a novel neural network architecture for improving generalization. Simulation results demonstrate that our proposed GMORL scheme enhances the hypervolume of the Pareto front by up to 121.0% compared to benchmarks. Our code are avavilable at https://github.com/gracefulning/Generalizable-Pareto-Optimal-Offloading-with-Reinforcement-Learning-in-Mobile-Edge-Computing

Learning a policy with great generalization to unseen environments remains challenging but critical in visual reinforcement learning. Despite the success of augmentation combination in the supervised learning generalization, naively applying it to visual RL algorithms may damage the training efficiency, suffering from serve performance degradation. In this paper, we first conduct qualitative analysis and illuminate the main causes: (i) high-variance gradient magnitudes and (ii) gradient conflicts existed in various augmentation methods. To alleviate these issues, we propose a general policy gradient optimization framework, named Conflict-aware Gradient Agreement Augmentation (CG2A), and better integrate augmentation combination into visual RL algorithms to address the generalization bias. In particular, CG2A develops a Gradient Agreement Solver to adaptively balance the varying gradient magnitudes, and introduces a Soft Gradient Surgery strategy to alleviate the gradient conflicts. Extensive experiments demonstrate that CG2A significantly improves the generalization performance and sample efficiency of visual RL algorithms.

Travel planning is a sophisticated decision-making process that requires synthesizing multifaceted information to construct itineraries. However, existing travel planning approaches face several challenges: (1) Pruning candidate points of interest (POIs) while maintaining a high recall rate; (2) A single reasoning path restricts the exploration capability within the feasible solution space for travel planning; (3) Simultaneously optimizing hard constraints and soft constraints remains a significant difficulty. To address these challenges, we propose TourPlanner, a comprehensive framework featuring multi-path reasoning and constraint-gated reinforcement learning. Specifically, we first introduce a Personalized Recall and Spatial Optimization (PReSO) workflow to construct spatially-aware candidate POIs' set. Subsequently, we propose Competitive consensus Chain-of-Thought (CCoT), a multi-path reasoning paradigm that improves the ability of exploring the feasible solution space. To further refine the plan, we integrate a sigmoid-based gating mechanism into the reinforcement learning stage, which dynamically prioritizes soft-constraint satisfaction only after hard constraints are met. Experimental results on travel planning benchmarks demonstrate that TourPlanner achieves state-of-the-art performance, significantly surpassing existing methods in both feasibility and user-preference alignment.

Randomized ensembled double Q-learning (REDQ) (Chen et al., 2021b) has recently achieved state-of-the-art sample efficiency on continuous-action reinforcement learning benchmarks. This superior sample efficiency is made possible by using a large Q-function ensemble. However, REDQ is much less computationally efficient than non-ensemble counterparts such as Soft Actor-Critic (SAC) (Haarnoja et al., 2018a). To make REDQ more computationally efficient, we propose a method of improving computational efficiency called DroQ, which is a variant of REDQ that uses a small ensemble of dropout Q-functions. Our dropout Q-functions are simple Q-functions equipped with dropout connection and layer normalization. Despite its simplicity of implementation, our experimental results indicate that DroQ is doubly (sample and computationally) efficient. It achieved comparable sample efficiency with REDQ, much better computational efficiency than REDQ, and comparable computational efficiency with that of SAC.

Reinforcement Learning with Verifiable Rewards (RLVR) has propelled Large Language Models in complex reasoning, yet its scalability is often hindered by a training bottleneck where performance plateaus as policy entropy collapses, signaling a loss of exploration. Previous methods typically address this by maintaining high policy entropy, yet the precise mechanisms that govern meaningful exploration have remained underexplored. Our analysis suggests that an unselective focus on entropy risks amplifying irrelevant tokens and destabilizing training. This paper investigates the exploration dynamics within RLVR and identifies a key issue: the gradual elimination of valuable low-probability exploratory tokens, which we term \textit{reasoning sparks}. We find that while abundant in pre-trained models, these sparks are systematically extinguished during RLVR due to over-penalization, leading to a degeneracy in exploration. To address this, we introduce Low-probability Regularization (Lp-Reg). Its core mechanism regularizes the policy towards a heuristic proxy distribution. This proxy is constructed by filtering out presumed noise tokens and re-normalizing the distribution over the remaining candidates. The result is a less-noisy proxy where the probability of reasoning sparks is amplified, which then serves as a soft regularization target to shield these valuable tokens from elimination via KL divergence. Experiments show that Lp-Reg enables stable on-policy training for around 1,000 steps, a regime where baseline entropy-control methods collapse. This sustained exploration leads to state-of-the-art performance, achieving a 60.17% average accuracy on five math benchmarks, an improvement of 2.66% over prior methods. Code is available at https://github.com/CarlanLark/Lp-Reg.

It is desired to equip robots with the capability of interacting with various soft materials as they are ubiquitous in the real world. While physics simulations are one of the predominant methods for data collection and robot training, simulating soft materials presents considerable challenges. Specifically, it is significantly more costly than simulating rigid objects in terms of simulation speed and storage requirements. These limitations typically restrict the scope of studies on soft materials to small and bounded areas, thereby hindering the learning of skills in broader spaces. To address this issue, we introduce UBSoft, a new simulation platform designed to support unbounded soft environments for robot skill acquisition. Our platform utilizes spatially adaptive resolution scales, where simulation resolution dynamically adjusts based on proximity to active robotic agents. Our framework markedly reduces the demand for extensive storage space and computation costs required for large-scale scenarios involving soft materials. We also establish a set of benchmark tasks in our platform, including both locomotion and manipulation tasks, and conduct experiments to evaluate the efficacy of various reinforcement learning algorithms and trajectory optimization techniques, both gradient-based and sampling-based. Preliminary results indicate that sampling-based trajectory optimization generally achieves better results for obtaining one trajectory to solve the task. Additionally, we conduct experiments in real-world environments to demonstrate that advancements made in our UBSoft simulator could translate to improved robot interactions with large-scale soft material. More videos can be found at https://vis-www.cs.umass.edu/ubsoft/.

Diffusion models are powerful generative models that allow for precise control over the characteristics of the generated samples. While these diffusion models trained on large datasets have achieved success, there is often a need to introduce additional controls in downstream fine-tuning processes, treating these powerful models as pre-trained diffusion models. This work presents a novel method based on reinforcement learning (RL) to add such controls using an offline dataset comprising inputs and labels. We formulate this task as an RL problem, with the classifier learned from the offline dataset and the KL divergence against pre-trained models serving as the reward functions. Our method, CTRL (Conditioning pre-Trained diffusion models with Reinforcement Learning), produces soft-optimal policies that maximize the abovementioned reward functions. We formally demonstrate that our method enables sampling from the conditional distribution with additional controls during inference. Our RL-based approach offers several advantages over existing methods. Compared to classifier-free guidance, it improves sample efficiency and can greatly simplify dataset construction by leveraging conditional independence between the inputs and additional controls. Additionally, unlike classifier guidance, it eliminates the need to train classifiers from intermediate states to additional controls. The code is available at https://github.com/zhaoyl18/CTRL.

Deep reinforcement learning (DRL) has successfully solved various problems recently, typically with a unimodal policy representation. However, grasping distinguishable skills for some tasks with non-unique optima can be essential for further improving its learning efficiency and performance, which may lead to a multimodal policy represented as a mixture-of-experts (MOE). To our best knowledge, present DRL algorithms for general utility do not deploy this method as policy function approximators due to the potential challenge in its differentiability for policy learning. In this work, we propose a probabilistic mixture-of-experts (PMOE) implemented with a Gaussian mixture model (GMM) for multimodal policy, together with a novel gradient estimator for the indifferentiability problem, which can be applied in generic off-policy and on-policy DRL algorithms using stochastic policies, e.g., Soft Actor-Critic (SAC) and Proximal Policy Optimisation (PPO). Experimental results testify the advantage of our method over unimodal polices and two different MOE methods, as well as a method of option frameworks, based on the above two types of DRL algorithms, on six MuJoCo tasks. Different gradient estimations for GMM like the reparameterisation trick (Gumbel-Softmax) and the score-ratio trick are also compared with our method. We further empirically demonstrate the distinguishable primitives learned with PMOE and show the benefits of our method in terms of exploration.

Deep reinforcement learning policies, despite their outstanding efficiency in simulated visual control tasks, have shown disappointing ability to generalize across disturbances in the input training images. Changes in image statistics or distracting background elements are pitfalls that prevent generalization and real-world applicability of such control policies. We elaborate on the intuition that a good visual policy should be able to identify which pixels are important for its decision, and preserve this identification of important sources of information across images. This implies that training of a policy with small generalization gap should focus on such important pixels and ignore the others. This leads to the introduction of saliency-guided Q-networks (SGQN), a generic method for visual reinforcement learning, that is compatible with any value function learning method. SGQN vastly improves the generalization capability of Soft Actor-Critic agents and outperforms existing stateof-the-art methods on the Deepmind Control Generalization benchmark, setting a new reference in terms of training efficiency, generalization gap, and policy interpretability.

Reinforcement learning (RL) plays an increasingly important role in enhancing the reasoning capabilities of large language models (LLMs), yet stable and performant policy optimization remains challenging. Token-level importance ratios often exhibit high variance-a phenomenon exacerbated in Mixture-of-Experts models-leading to unstable updates. Existing group-based policy optimization methods, such as GSPO and GRPO, alleviate this problem via hard clipping, making it difficult to maintain both stability and effective learning. We propose Soft Adaptive Policy Optimization (SAPO), which replaces hard clipping with a smooth, temperature-controlled gate that adaptively attenuates off-policy updates while preserving useful learning signals. Compared with GSPO and GRPO, SAPO is both sequence-coherent and token-adaptive. Like GSPO, SAPO maintains sequence-level coherence, but its soft gating forms a continuous trust region that avoids the brittle hard clipping band used in GSPO. When a sequence contains a few highly off-policy tokens, GSPO suppresses all gradients for that sequence, whereas SAPO selectively down-weights only the offending tokens and preserves the learning signal from the near-on-policy ones, improving sample efficiency. Relative to GRPO, SAPO replaces hard token-level clipping with smooth, temperature-controlled scaling, enabling more informative and stable updates. Empirical results on mathematical reasoning benchmarks indicate that SAPO exhibits improved training stability and higher Pass@1 performance under comparable training budgets. Moreover, we employ SAPO to train the Qwen3-VL model series, demonstrating that SAPO yields consistent performance gains across diverse tasks and different model sizes. Overall, SAPO provides a more reliable, scalable, and effective optimization strategy for RL training of LLMs.

The use of continuous instead of discrete tokens during the Chain-of-Thought (CoT) phase of reasoning LLMs has garnered attention recently, based on the intuition that a continuous mixture of discrete tokens could simulate a superposition of several reasoning paths simultaneously. Theoretical results have formally proven that continuous tokens have much greater expressivity and can solve specific problems more efficiently. However, practical use of continuous tokens has been limited by strong training difficulties: previous works either just use continuous tokens at inference time on a pre-trained discrete-token model, or must distill the continuous CoT from ground-truth discrete CoTs and face computational costs that limit the CoT to very few tokens. This is the first work introducing a scalable method to learn continuous CoTs via reinforcement learning (RL), without distilling from reference discrete CoTs. We use "soft" tokens: mixtures of tokens together with noise on the input embedding to provide RL exploration. Computational overhead is minimal, enabling us to learn continuous CoTs with hundreds of tokens. On math reasoning benchmarks with Llama and Qwen models up to 8B, training with continuous CoTs match discrete-token CoTs for pass@1 and surpass them for pass@32, showing greater CoT diversity. In systematic comparisons, the best-performing scenario is to train with continuous CoT tokens then use discrete tokens for inference, meaning the "soft" models can be deployed in a standard way. Finally, we show continuous CoT RL training better preserves the predictions of the base model on out-of-domain tasks, thus providing a softer touch to the base model.

Deep Reinforcement Learning is emerging as a promising approach for the continuous control task of robotic arm movement. However, the challenges of learning robust and versatile control capabilities are still far from being resolved for real-world applications, mainly because of two common issues of this learning paradigm: the exploration strategy and the slow learning speed, sometimes known as "the curse of dimensionality". This work aims at exploring and assessing the advantages of the application of Quantum Computing to one of the state-of-art Reinforcement Learning techniques for continuous control - namely Soft Actor-Critic. Specifically, the performance of a Variational Quantum Soft Actor-Critic on the movement of a virtual robotic arm has been investigated by means of digital simulations of quantum circuits. A quantum advantage over the classical algorithm has been found in terms of a significant decrease in the amount of required parameters for satisfactory model training, paving the way for further promising developments.

Reinforcement learning (RL) has shown remarkable success in solving complex decision-making and control tasks. However, many model-free RL algorithms experience performance degradation due to inaccurate value estimation, particularly the overestimation of Q-values, which can lead to suboptimal policies. To address this issue, we previously proposed the Distributional Soft Actor-Critic (DSAC or DSACv1), an off-policy RL algorithm that enhances value estimation accuracy by learning a continuous Gaussian value distribution. Despite its effectiveness, DSACv1 faces challenges such as training instability and sensitivity to reward scaling, caused by high variance in critic gradients due to return randomness. In this paper, we introduce three key refinements to DSACv1 to overcome these limitations and further improve Q-value estimation accuracy: expected value substitution, twin value distribution learning, and variance-based critic gradient adjustment. The enhanced algorithm, termed DSAC with Three refinements (DSAC-T or DSACv2), is systematically evaluated across a diverse set of benchmark tasks. Without the need for task-specific hyperparameter tuning, DSAC-T consistently matches or outperforms leading model-free RL algorithms, including SAC, TD3, DDPG, TRPO, and PPO, in all tested environments. Additionally, DSAC-T ensures a stable learning process and maintains robust performance across varying reward scales. Its effectiveness is further demonstrated through real-world application in controlling a wheeled robot, highlighting its potential for deployment in practical robotic tasks.

Model-free deep reinforcement learning (RL) algorithms have been successfully applied to a range of challenging sequential decision making and control tasks. However, these methods typically suffer from two major challenges: high sample complexity and brittleness to hyperparameters. Both of these challenges limit the applicability of such methods to real-world domains. In this paper, we describe Soft Actor-Critic (SAC), our recently introduced off-policy actor-critic algorithm based on the maximum entropy RL framework. In this framework, the actor aims to simultaneously maximize expected return and entropy. That is, to succeed at the task while acting as randomly as possible. We extend SAC to incorporate a number of modifications that accelerate training and improve stability with respect to the hyperparameters, including a constrained formulation that automatically tunes the temperature hyperparameter. We systematically evaluate SAC on a range of benchmark tasks, as well as real-world challenging tasks such as locomotion for a quadrupedal robot and robotic manipulation with a dexterous hand. With these improvements, SAC achieves state-of-the-art performance, outperforming prior on-policy and off-policy methods in sample-efficiency and asymptotic performance. Furthermore, we demonstrate that, in contrast to other off-policy algorithms, our approach is very stable, achieving similar performance across different random seeds. These results suggest that SAC is a promising candidate for learning in real-world robotics tasks.

Open-weight coding agents should hold a fundamental advantage over closed-source systems: they can be specialized to private codebases, encoding repository-specific information directly in their weights. Yet the cost and complexity of training has kept this advantage theoretical. We show it is now practical. We present Soft-Verified Efficient Repository Agents (SERA), an efficient method for training coding agents that enables the rapid and cheap creation of agents specialized to private codebases. Using only supervised finetuning (SFT), SERA achieves state-of-the-art results among fully open-source (open data, method, code) models while matching the performance of frontier open-weight models like Devstral-Small-2. Creating SERA models is 26x cheaper than reinforcement learning and 57x cheaper than previous synthetic data methods to reach equivalent performance. Our method, Soft Verified Generation (SVG), generates thousands of trajectories from a single code repository. Combined with cost-efficiency, this enables specialization to private codebases. Beyond repository specialization, we apply SVG to a larger corpus of codebases, generating over 200,000 synthetic trajectories. We use this dataset to provide detailed analysis of scaling laws, ablations, and confounding factors for training coding agents. Overall, we believe our work will greatly accelerate research on open coding agents and showcase the advantage of open-source models that can specialize to private codebases. We release SERA as the first model in Ai2's Open Coding Agents series, along with all our code, data, and Claude Code integration to support the research community.

Training stability remains a central challenge in reinforcement learning (RL) for large language models (LLMs). Policy staleness, asynchronous training, and mismatches between training and inference engines all cause the behavior policy to diverge from the current policy, risking training collapse. Importance sampling provides a principled correction for this distribution shift but suffers from high variance; existing remedies such as token-level clipping and sequence-level normalization lack a unified theoretical foundation. We propose Variational sEquence-level Soft Policy Optimization (VESPO). By incorporating variance reduction into a variational formulation over proposal distributions, VESPO derives a closed-form reshaping kernel that operates directly on sequence-level importance weights without length normalization. Experiments on mathematical reasoning benchmarks show that VESPO maintains stable training under staleness ratios up to 64x and fully asynchronous execution, and delivers consistent gains across both dense and Mixture-of-Experts models. Code is available at https://github.com/FloyedShen/VESPO

Can Visual Language Models (VLMs) effectively capture human visual preferences? This work addresses this question by training VLMs to think about preferences at test time, employing reinforcement learning methods inspired by DeepSeek R1 and OpenAI O1. Using datasets such as ImageReward and Human Preference Score v2 (HPSv2), our models achieve accuracies of 64.9% on the ImageReward test set (trained on ImageReward official split) and 65.4% on HPSv2 (trained on approximately 25% of its data). These results match traditional encoder-based models while providing transparent reasoning and enhanced generalization. This approach allows to use not only rich VLM world knowledge, but also its potential to think, yielding interpretable outcomes that help decision-making processes. By demonstrating that human visual preferences reasonable by current VLMs, we introduce efficient soft-reward strategies for image ranking, outperforming simplistic selection or scoring methods. This reasoning capability enables VLMs to rank arbitrary images-regardless of aspect ratio or complexity-thereby potentially amplifying the effectiveness of visual Preference Optimization. By reducing the need for extensive markup while improving reward generalization and explainability, our findings can be a strong mile-stone that will enhance text-to-vision models even further.

Soft Actor-Critic is a state-of-the-art reinforcement learning algorithm for continuous action settings that is not applicable to discrete action settings. Many important settings involve discrete actions, however, and so here we derive an alternative version of the Soft Actor-Critic algorithm that is applicable to discrete action settings. We then show that, even without any hyperparameter tuning, it is competitive with the tuned model-free state-of-the-art on a selection of games from the Atari suite.

Training large language models (LLMs) with reinforcement learning (RL) methods such as PPO and GRPO commonly relies on ratio clipping to stabilise updates. While effective at preventing instability, clipping discards information and introduces gradient discontinuities. We propose Probability Smoothing Policy Optimisation (PSPO), which smooths the current policy's probabilities toward the old (behaviour) policy before computing the importance ratio, analogous to label smoothing. Unlike clipping, PSPO preserves gradient signal, while interpolation toward the old policy creates a soft trust region that discourages large, destabilising updates, with formal guarantees. We instantiate PSPO within GRPO (GR-PSPO) and fine-tune Qwen2.5-0.5B and Qwen2.5-1.5B on GSM8K, evaluating on GSM8K test and the cross-dataset generalisation on SVAMP, ASDiv, and MATH-500. Relative to unclipped GRPO (single iteration; no data reuse, ratio always = 1), GR-PSPO achieves similar performance but improves the reasoning leading to clearer and more concise responses which are more logical. Compared to clipped GRPO, GR-PSPO substantially improves performance both the 0.5B and 1.5B models, with a boost of over 20% on GSM8K (39.7% vs. 17.6% for 0.5B, 59.4% vs. 37.8% for 1.5B).

Chain-of-thought (CoT) reasoning sometimes fails to faithfully reflect the true computation of a large language model (LLM), hampering its utility in explaining how LLMs arrive at their answers. Moreover, optimizing for faithfulness and interpretability in reasoning often degrades task performance. To address this tradeoff and improve CoT faithfulness, we propose Reasoning Execution by Multiple Listeners (REMUL), a multi-party reinforcement learning approach. REMUL builds on the hypothesis that reasoning traces which other parties can follow will be more faithful. A speaker model generates a reasoning trace, which is truncated and passed to a pool of listener models who "execute" the trace, continuing the trace to an answer. Speakers are rewarded for producing reasoning that is clear to listeners, with additional correctness regularization via masked supervised finetuning to counter the tradeoff between faithfulness and performance. On multiple reasoning benchmarks (BIG-Bench Extra Hard, MuSR, ZebraLogicBench, and FOLIO), REMUL consistently and substantially improves three measures of faithfulness -- hint attribution, early answering area over the curve (AOC), and mistake injection AOC -- while also improving accuracy. Our analysis finds that these gains are robust across training domains, translate to legibility gains, and are associated with shorter and more direct CoTs.

Unlike human reasoning in abstract conceptual spaces, large language models (LLMs) typically reason by generating discrete tokens, which potentially limit their expressive power. The recent work Soft Thinking has shown that LLMs' latent reasoning via soft concepts is a promising direction, but LLMs are trained on discrete tokens. To reduce this gap between the soft concepts in reasoning and the discrete tokens in training, we propose Soft Concept Mixing (SCM), a soft concept aware training scheme that directly exposes the model to soft representations during training. Specifically, SCM constructs a soft concept vector by forming a probability-weighted average of embeddings. Then, this vector is mixed into the model's hidden states, which embody rich contextual information. Finally, the entire latent reasoning process is optimized with Reinforcement Learning (RL). Experiments on five reasoning benchmarks demonstrate that SCM improves the reasoning performance of LLMs, and simultaneously maintains a stable training dynamic.

The past years have seen Large Language Models (LLMs) strive not only as generative models but also as agents solving textual sequential decision-making tasks. When facing complex environments where their zero-shot abilities are insufficient, recent work showed online Reinforcement Learning (RL) could be used for the LLM agent to discover and learn efficient strategies interactively. However, most prior work sticks to on-policy algorithms, which greatly reduces the scope of methods such agents could use for both exploration and exploitation, such as experience replay and hindsight relabeling. Yet, such methods may be key for LLM learning agents, and in particular when designing autonomous intrinsically motivated agents sampling and pursuing their own goals (i.e. autotelic agents). This paper presents and studies an adaptation of Soft Actor-Critic and hindsight relabeling to LLM agents. Our method not only paves the path towards autotelic LLM agents that learn online but can also outperform on-policy methods in more classic multi-goal RL environments.

We study the adaption of Soft Actor-Critic (SAC), which is considered as a state-of-the-art reinforcement learning (RL) algorithm, from continuous action space to discrete action space. We revisit vanilla discrete SAC and provide an in-depth understanding of its Q value underestimation and performance instability issues when applied to discrete settings. We thereby propose Stable Discrete SAC (SDSAC), an algorithm that leverages entropy-penalty and double average Q-learning with Q-clip to address these issues. Extensive experiments on typical benchmarks with discrete action space, including Atari games and a large-scale MOBA game, show the efficacy of our proposed method. Our code is at: https://github.com/coldsummerday/SD-SAC.git.

Both the design and control of a robot play equally important roles in its task performance. However, while optimal control is well studied in the machine learning and robotics community, less attention is placed on finding the optimal robot design. This is mainly because co-optimizing design and control in robotics is characterized as a challenging problem, and more importantly, a comprehensive evaluation benchmark for co-optimization does not exist. In this paper, we propose Evolution Gym, the first large-scale benchmark for co-optimizing the design and control of soft robots. In our benchmark, each robot is composed of different types of voxels (e.g., soft, rigid, actuators), resulting in a modular and expressive robot design space. Our benchmark environments span a wide range of tasks, including locomotion on various types of terrains and manipulation. Furthermore, we develop several robot co-evolution algorithms by combining state-of-the-art design optimization methods and deep reinforcement learning techniques. Evaluating the algorithms on our benchmark platform, we observe robots exhibiting increasingly complex behaviors as evolution progresses, with the best evolved designs solving many of our proposed tasks. Additionally, even though robot designs are evolved autonomously from scratch without prior knowledge, they often grow to resemble existing natural creatures while outperforming hand-designed robots. Nevertheless, all tested algorithms fail to find robots that succeed in our hardest environments. This suggests that more advanced algorithms are required to explore the high-dimensional design space and evolve increasingly intelligent robots -- an area of research in which we hope Evolution Gym will accelerate progress. Our website with code, environments, documentation, and tutorials is available at http://evogym.csail.mit.edu.

In this paper we deploy for the first time Reinforcement-Learning algorithms in the context of the conformal-bootstrap programme to obtain numerical solutions of conformal field theories (CFTs). As an illustration, we use a soft Actor-Critic algorithm and find approximate solutions to the truncated crossing equations of two-dimensional CFTs, successfully identifying well-known theories like the 2D Ising model and the 2D CFT of a compactified scalar. Our methods can perform efficient high-dimensional searches that can be used to study arbitrary (unitary or non-unitary) CFTs in any spacetime dimension.

Reinforcement learning (RL) with verifiable rewards (RLVR) has shown promising results in mathematical reasoning and coding tasks where well-structured reference answers are available. However, its applicability to broader domains remains underexplored. In this work, we study the extension of RLVR to more diverse domains such as medicine, chemistry, psychology, and economics. We observe high agreement in binary judgments across different large language models (LLMs) when objective reference answers exist, which challenges the necessity of large-scale annotation for training domain-specific reward models. To address the limitations of binary rewards when handling unstructured reference answers, we further incorporate model-based soft scoring into RLVR to improve its flexibility. Our experiments show that a distilled generative reward model can serve as an effective cross-domain verifier, providing reliable reward signals for RL without requiring domain-specific annotations. By fine-tuning a base 7B model using various RL algorithms against our reward model, we obtain policies that outperform state-of-the-art open-source aligned LLMs such as Qwen2.5-72B-Instruct and DeepSeek-R1-Distill-Qwen-32B by a large margin, across domains in free-form answer settings. This also strengthens RLVR's robustness and scalability, highlighting its potential for real-world applications with noisy or weak labels.

A central belief in scaling reinforcement learning with verifiable rewards for instruction following (IF) tasks is that, a diverse mixture of verifiable hard and unverifiable soft constraints is essential for generalizing to unseen instructions. In this work, we challenge this prevailing consensus through a systematic empirical investigation. Counter-intuitively, we find that models trained on hard-only constraints consistently outperform those trained on mixed datasets. Extensive experiments reveal that reward precision, rather than constraint diversity, is the primary driver of effective alignment. The LLM judge suffers from a low recall rate in detecting false response, which leads to severe reward hacking, thereby undermining the benefits of diversity. Furthermore, analysis of the attention mechanism reveals that high-precision rewards develop a transferable meta-skill for IF. Motivated by these insights, we propose a simple yet effective data-centric refinement strategy that prioritizes reward precision. Evaluated on five benchmarks, our approach outperforms competitive baselines by 13.4\% in performance while achieving a 58\% reduction in training time, maintaining strong generalization beyond instruction following. Our findings advocate for a paradigm shift: moving away from the indiscriminate pursuit of data diversity toward high-precision rewards.

Reinforcement Learning (RL) plays a crucial role in aligning large language models (LLMs) with human preferences and improving their ability to perform complex tasks. However, current approaches either require significant computational resources due to the use of multiple models and extensive online sampling for training (e.g., PPO) or are framed as bandit problems (e.g., DPO, DRO), which often struggle with multi-step reasoning tasks, such as math problem-solving and complex reasoning that involve long chains of thought. To overcome these limitations, we introduce Direct Q-function Optimization (DQO), which formulates the response generation process as a Markov Decision Process (MDP) and utilizes the soft actor-critic (SAC) framework to optimize a Q-function directly parameterized by the language model. The MDP formulation of DQO offers structural advantages over bandit-based methods, enabling more effective process supervision. Experimental results on two math problem-solving datasets, GSM8K and MATH, demonstrate that DQO outperforms previous methods, establishing it as a promising offline reinforcement learning approach for aligning language models.

The recent rapid progress in (self) supervised learning models is in large part predicted by empirical scaling laws: a model's performance scales proportionally to its size. Analogous scaling laws remain elusive for reinforcement learning domains, however, where increasing the parameter count of a model often hurts its final performance. In this paper, we demonstrate that incorporating Mixture-of-Expert (MoE) modules, and in particular Soft MoEs (Puigcerver et al., 2023), into value-based networks results in more parameter-scalable models, evidenced by substantial performance increases across a variety of training regimes and model sizes. This work thus provides strong empirical evidence towards developing scaling laws for reinforcement learning.

The use of deep neural networks in reinforcement learning (RL) often suffers from performance degradation as model size increases. While soft mixtures of experts (SoftMoEs) have recently shown promise in mitigating this issue for online RL, the reasons behind their effectiveness remain largely unknown. In this work we provide an in-depth analysis identifying the key factors driving this performance gain. We discover the surprising result that tokenizing the encoder output, rather than the use of multiple experts, is what is behind the efficacy of SoftMoEs. Indeed, we demonstrate that even with an appropriately scaled single expert, we are able to maintain the performance gains, largely thanks to tokenization.

Large language models often solve complex reasoning tasks more effectively with Chain-of-Thought (CoT), but at the cost of long, low-bandwidth token sequences. Humans, by contrast, often reason softly by maintaining a distribution over plausible next steps. Motivated by this, we propose Multiplex Thinking, a stochastic soft reasoning mechanism that, at each thinking step, samples K candidate tokens and aggregates their embeddings into a single continuous multiplex token. This preserves the vocabulary embedding prior and the sampling dynamics of standard discrete generation, while inducing a tractable probability distribution over multiplex rollouts. Consequently, multiplex trajectories can be directly optimized with on-policy reinforcement learning (RL). Importantly, Multiplex Thinking is self-adaptive: when the model is confident, the multiplex token is nearly discrete and behaves like standard CoT; when it is uncertain, it compactly represents multiple plausible next steps without increasing sequence length. Across challenging math reasoning benchmarks, Multiplex Thinking consistently outperforms strong discrete CoT and RL baselines from Pass@1 through Pass@1024, while producing shorter sequences. The code and checkpoints are available at https://github.com/GMLR-Penn/Multiplex-Thinking.

Large-scale pre-trained language models (LLMs) have demonstrated exceptional performance in various natural language processing (NLP) tasks. However, the massive size of these models poses huge challenges for their deployment in real-world applications. While numerous model compression techniques have been proposed, most of them are not well-suited for achieving extreme model compression when there is a significant gap in model scale. In this paper, we introduce a novel compression paradigm called Retrieval-based Knowledge Transfer (RetriKT), which effectively transfers the knowledge of LLMs to extremely small-scale models (e.g., 1%). In particular, our approach extracts knowledge from LLMs to construct a knowledge store, from which the small-scale model can retrieve relevant information and leverage it for effective inference. To improve the quality of the model, soft prompt tuning and Proximal Policy Optimization (PPO) reinforcement learning techniques are employed. Extensive experiments are conducted on low-resource tasks from SuperGLUE and GLUE benchmarks. The results demonstrate that the proposed approach significantly enhances the performance of small-scale models by leveraging the knowledge from LLMs.

Despite the success of Random Network Distillation (RND) in various domains, it was shown as not discriminative enough to be used as an uncertainty estimator for penalizing out-of-distribution actions in offline reinforcement learning. In this paper, we revisit these results and show that, with a naive choice of conditioning for the RND prior, it becomes infeasible for the actor to effectively minimize the anti-exploration bonus and discriminativity is not an issue. We show that this limitation can be avoided with conditioning based on Feature-wise Linear Modulation (FiLM), resulting in a simple and efficient ensemble-free algorithm based on Soft Actor-Critic. We evaluate it on the D4RL benchmark, showing that it is capable of achieving performance comparable to ensemble-based methods and outperforming ensemble-free approaches by a wide margin.

3D referring expression comprehension (3DREC) and segmentation (3DRES) have overlapping objectives, indicating their potential for collaboration. However, existing collaborative approaches predominantly depend on the results of one task to make predictions for the other, limiting effective collaboration. We argue that employing separate branches for 3DREC and 3DRES tasks enhances the model's capacity to learn specific information for each task, enabling them to acquire complementary knowledge. Thus, we propose the MCLN framework, which includes independent branches for 3DREC and 3DRES tasks. This enables dedicated exploration of each task and effective coordination between the branches. Furthermore, to facilitate mutual reinforcement between these branches, we introduce a Relative Superpoint Aggregation (RSA) module and an Adaptive Soft Alignment (ASA) module. These modules significantly contribute to the precise alignment of prediction results from the two branches, directing the module to allocate increased attention to key positions. Comprehensive experimental evaluation demonstrates that our proposed method achieves state-of-the-art performance on both the 3DREC and 3DRES tasks, with an increase of 2.05% in Acc@0.5 for 3DREC and 3.96% in mIoU for 3DRES.

Existing imitation learning methods mainly focus on making an agent effectively mimic a demonstrated behavior, but do not address the potential contradiction between the behavior style and the objective of a task. There is a general lack of efficient methods that allow an agent to partially imitate a demonstrated behavior to varying degrees, while completing the main objective of a task. In this paper we propose a method called Regularized Soft Actor-Critic which formulates the main task and the imitation task under the Constrained Markov Decision Process framework (CMDP). The main task is defined as the maximum entropy objective used in Soft Actor-Critic (SAC) and the imitation task is defined as a constraint. We evaluate our method on continuous control tasks relevant to video games applications.

Markov Decision Processes (MDPs) are a formal framework for modeling and solving sequential decision-making problems. In finite-time horizons such problems are relevant for instance for optimal stopping or specific supply chain problems, but also in the training of large language models. In contrast to infinite horizon MDPs optimal policies are not stationary, policies must be learned for every single epoch. In practice all parameters are often trained simultaneously, ignoring the inherent structure suggested by dynamic programming. This paper introduces a combination of dynamic programming and policy gradient called dynamic policy gradient, where the parameters are trained backwards in time. For the tabular softmax parametrisation we carry out the convergence analysis for simultaneous and dynamic policy gradient towards global optima, both in the exact and sampled gradient settings without regularisation. It turns out that the use of dynamic policy gradient training much better exploits the structure of finite-time problems which is reflected in improved convergence bounds.

Reinforcement learning is a framework for learning to act sequentially in an unknown environment. We propose a natural approach for modeling policy structure in policy gradients. The key idea is to optimize for a subset of future rewards: smaller subsets represent simpler policies, which can be learned more reliably because their empirical gradient estimates are more accurate. Our approach allows for modeling and comparison of different policy classes, including full planning, greedy, K-step lookahead, and segment policies. We evaluate the policies empirically on multiple persona-alignment conversational problems. Different policies excel in different problems, reflecting their different characteristics and highlighting the importance of our studied policy class.

Reinforcement learning is the method of choice to train models in sampling-based setups with binary outcome feedback, such as navigation, code generation, and mathematical problem solving. In such settings, models implicitly induce a likelihood over correct rollouts. However, we observe that reinforcement learning does not maximize this likelihood, and instead optimizes only a lower-order approximation. Inspired by this observation, we introduce Maximum Likelihood Reinforcement Learning (MaxRL), a sampling-based framework to approximate maximum likelihood using reinforcement learning techniques. MaxRL addresses the challenges of non-differentiable sampling by defining a compute-indexed family of sample-based objectives that interpolate between standard reinforcement learning and exact maximum likelihood as additional sampling compute is allocated. The resulting objectives admit a simple, unbiased policy-gradient estimator and converge to maximum likelihood optimization in the infinite-compute limit. Empirically, we show that MaxRL Pareto-dominates existing methods in all models and tasks we tested, achieving up to 20x test-time scaling efficiency gains compared to its GRPO-trained counterpart. We also observe MaxRL to scale better with additional data and compute. Our results suggest MaxRL is a promising framework for scaling RL training in correctness based settings.

The fine-tuning of pre-trained large language models (LLMs) using reinforcement learning (RL) is generally formulated as direct policy optimization. This approach was naturally favored as it efficiently improves a pretrained LLM, seen as an initial policy. Another RL paradigm, Q-learning methods, has received far less attention in the LLM community while demonstrating major success in various non-LLM RL tasks. In particular, Q-learning effectiveness comes from its sample efficiency and ability to learn offline, which is particularly valuable given the high computational cost of sampling with LLMs. However, naively applying a Q-learning-style update to the model's logits is ineffective due to the specificity of LLMs. Our core contribution is to derive theoretically grounded loss functions from Bellman equations to adapt Q-learning methods to LLMs. To do so, we carefully adapt insights from the RL literature to account for LLM-specific characteristics, ensuring that the logits become reliable Q-value estimates. We then use this loss to build a practical algorithm, ShiQ for Shifted-Q, that supports off-policy, token-wise learning while remaining simple to implement. Finally, we evaluate ShiQ on both synthetic data and real-world benchmarks, e.g., UltraFeedback and BFCL-V3, demonstrating its effectiveness in both single-turn and multi-turn LLM settings

Soft Actor Critic (SAC) algorithms show remarkable performance in complex simulated environments. A key element of SAC networks is entropy regularization, which prevents the SAC actor from optimizing against fine grained features, oftentimes transient, of the state-action value function. This results in better sample efficiency during early training. We take this idea one step further by artificially bandlimiting the target critic spatial resolution through the addition of a convolutional filter. We derive the closed form solution in the linear case and show that bandlimiting reduces the interdependency between the low and high frequency components of the state-action value approximation, allowing the critic to learn faster. In experiments, the bandlimited SAC outperformed the classic twin-critic SAC in a number of Gym environments, and displayed more stability in returns. We derive novel insights about SAC by adding a stochastic noise disturbance, a technique that is increasingly being used to learn robust policies that transfer well to the real world counterparts.

We present a general convergent class of reinforcement learning algorithms that is founded on two distinct principles: (1) mapping value estimates to a different space using arbitrary functions from a broad class, and (2) linearly decomposing the reward signal into multiple channels. The first principle enables incorporating specific properties into the value estimator that can enhance learning. The second principle, on the other hand, allows for the value function to be represented as a composition of multiple utility functions. This can be leveraged for various purposes, e.g. dealing with highly varying reward scales, incorporating a priori knowledge about the sources of reward, and ensemble learning. Combining the two principles yields a general blueprint for instantiating convergent algorithms by orchestrating diverse mapping functions over multiple reward channels. This blueprint generalizes and subsumes algorithms such as Q-Learning, Log Q-Learning, and Q-Decomposition. In addition, our convergence proof for this general class relaxes certain required assumptions in some of these algorithms. Based on our theory, we discuss several interesting configurations as special cases. Finally, to illustrate the potential of the design space that our theory opens up, we instantiate a particular algorithm and evaluate its performance on the Atari suite.

Training reinforcement learning (RL) agents on robotic tasks typically requires a large number of training samples. This is because training data often consists of noisy trajectories, whether from exploration or human-collected demonstrations, making it difficult to learn value functions that understand the effect of taking each action. On the other hand, recent behavior-cloning (BC) approaches have shown that predicting a sequence of actions enables policies to effectively approximate noisy, multi-modal distributions of expert demonstrations. Can we use a similar idea for improving RL on robotic tasks? In this paper, we introduce a novel RL algorithm that learns a critic network that outputs Q-values over a sequence of actions. By explicitly training the value functions to learn the consequence of executing a series of current and future actions, our algorithm allows for learning useful value functions from noisy trajectories. We study our algorithm across various setups with sparse and dense rewards, and with or without demonstrations, spanning mobile bi-manual manipulation, whole-body control, and tabletop manipulation tasks from BiGym, HumanoidBench, and RLBench. We find that, by learning the critic network with action sequences, our algorithm outperforms various RL and BC baselines, in particular on challenging humanoid control tasks.

While many real-world problems that might benefit from reinforcement learning, these problems rarely fit into the MDP mold: interacting with the environment is often expensive and specifying reward functions is challenging. Motivated by these challenges, prior work has developed data-driven approaches that learn entirely from samples from the transition dynamics and examples of high-return states. These methods typically learn a reward function from high-return states, use that reward function to label the transitions, and then apply an offline RL algorithm to these transitions. While these methods can achieve good results on many tasks, they can be complex, often requiring regularization and temporal difference updates. In this paper, we propose a method for offline, example-based control that learns an implicit model of multi-step transitions, rather than a reward function. We show that this implicit model can represent the Q-values for the example-based control problem. Across a range of state-based and image-based offline control tasks, our method outperforms baselines that use learned reward functions; additional experiments demonstrate improved robustness and scaling with dataset size.

Risk-sensitive reinforcement learning (RL) has become a popular tool to control the risk of uncertain outcomes and ensure reliable performance in various sequential decision-making problems. While policy gradient methods have been developed for risk-sensitive RL, it remains unclear if these methods enjoy the same global convergence guarantees as in the risk-neutral case. In this paper, we consider a class of dynamic time-consistent risk measures, called Expected Conditional Risk Measures (ECRMs), and derive policy gradient updates for ECRM-based objective functions. Under both constrained direct parameterization and unconstrained softmax parameterization, we provide global convergence and iteration complexities of the corresponding risk-averse policy gradient algorithms. We further test risk-averse variants of REINFORCE and actor-critic algorithms to demonstrate the efficacy of our method and the importance of risk control.

Recent Reinforcement Learning (RL) algorithms making use of Kullback-Leibler (KL) regularization as a core component have shown outstanding performance. Yet, only little is understood theoretically about why KL regularization helps, so far. We study KL regularization within an approximate value iteration scheme and show that it implicitly averages q-values. Leveraging this insight, we provide a very strong performance bound, the very first to combine two desirable aspects: a linear dependency to the horizon (instead of quadratic) and an error propagation term involving an averaging effect of the estimation errors (instead of an accumulation effect). We also study the more general case of an additional entropy regularizer. The resulting abstract scheme encompasses many existing RL algorithms. Some of our assumptions do not hold with neural networks, so we complement this theoretical analysis with an extensive empirical study.

Reinforcement learning (RL) theory has largely focused on proving minimax sample complexity bounds. These require strategic exploration algorithms that use relatively limited function classes for representing the policy or value function. Our goal is to explain why deep RL algorithms often perform well in practice, despite using random exploration and much more expressive function classes like neural networks. Our work arrives at an explanation by showing that many stochastic MDPs can be solved by performing only a few steps of value iteration on the random policy's Q function and then acting greedily. When this is true, we find that it is possible to separate the exploration and learning components of RL, making it much easier to analyze. We introduce a new RL algorithm, SQIRL, that iteratively learns a near-optimal policy by exploring randomly to collect rollouts and then performing a limited number of steps of fitted-Q iteration over those rollouts. Any regression algorithm that satisfies basic in-distribution generalization properties can be used in SQIRL to efficiently solve common MDPs. This can explain why deep RL works, since it is empirically established that neural networks generalize well in-distribution. Furthermore, SQIRL explains why random exploration works well in practice. We leverage SQIRL to derive instance-dependent sample complexity bounds for RL that are exponential only in an "effective horizon" of lookahead and on the complexity of the class used for function approximation. Empirically, we also find that SQIRL performance strongly correlates with PPO and DQN performance in a variety of stochastic environments, supporting that our theoretical analysis is predictive of practical performance. Our code and data are available at https://github.com/cassidylaidlaw/effective-horizon.

Large language models (LLMs) have shown promise in performing complex multi-step reasoning, yet they continue to struggle with mathematical reasoning, often making systematic errors. A promising solution is reinforcement learning (RL) guided by reward models, particularly those focusing on process rewards, which score each intermediate step rather than solely evaluating the final outcome. This approach is more effective at guiding policy models towards correct reasoning trajectories. In this work, we propose an entropy-regularized process reward model (ER-PRM) that integrates KL-regularized Markov Decision Processes (MDP) to balance policy optimization with the need to prevent the policy from shifting too far from its initial distribution. We derive a novel reward construction method based on the theoretical results. Our theoretical analysis shows that we could derive the optimal reward model from the initial policy sampling. Our empirical experiments on the MATH and GSM8K benchmarks demonstrate that ER-PRM consistently outperforms existing process reward models, achieving 1% improvement on GSM8K and 2-3% improvement on MATH under best-of-N evaluation, and more than 1% improvement under RLHF. These results highlight the efficacy of entropy-regularization in enhancing LLMs' reasoning capabilities.

In recent years, neural networks have enjoyed a renaissance as function approximators in reinforcement learning. Two decades after Tesauro's TD-Gammon achieved near top-level human performance in backgammon, the deep reinforcement learning algorithm DQN achieved human-level performance in many Atari 2600 games. The purpose of this study is twofold. First, we propose two activation functions for neural network function approximation in reinforcement learning: the sigmoid-weighted linear unit (SiLU) and its derivative function (dSiLU). The activation of the SiLU is computed by the sigmoid function multiplied by its input. Second, we suggest that the more traditional approach of using on-policy learning with eligibility traces, instead of experience replay, and softmax action selection with simple annealing can be competitive with DQN, without the need for a separate target network. We validate our proposed approach by, first, achieving new state-of-the-art results in both stochastic SZ-Tetris and Tetris with a small 10times10 board, using TD(λ) learning and shallow dSiLU network agents, and, then, by outperforming DQN in the Atari 2600 domain by using a deep Sarsa(λ) agent with SiLU and dSiLU hidden units.

Even though large language models are becoming increasingly capable, it is still unreasonable to expect them to excel at tasks that are under-represented on the Internet. Leveraging LLMs for specialized applications, particularly in niche programming languages and private domains, remains challenging and largely unsolved. In this work, we address this gap by presenting a comprehensive, open-source approach for adapting LLMs to the Q programming language, a popular tool in quantitative finance that is much less present on the Internet compared to Python, C, Java, and other ``mainstream" languages and is therefore not a strong suit of general-purpose AI models. We introduce a new Leetcode style evaluation dataset for Q, benchmark major frontier models on the dataset, then do pretraining, supervised fine tuning, and reinforcement learning to train a suite of reasoning and non-reasoning models based on the Qwen-2.5 series, spanning five parameter sizes (1.5B, 3B, 7B, 14B, 32B). Our best model achieves a pass@1 accuracy of 59 percent on our Q benchmark, surpassing the best-performing frontier model, Claude Opus-4 by 29.5 percent. Additionally, all models, even our 1.5B model, outperform GPT-4.1 on this task. In addition to releasing models, code, and data, we provide a detailed blueprint for dataset construction, model pretraining, supervised fine-tuning, and reinforcement learning. Our methodology is broadly applicable, and we discuss how these techniques can be extended to other tasks, including those where evaluation may rely on soft or subjective signals.

In long-horizon tasks, recent agents based on Large Language Models (LLMs) face a significant challenge that sparse, outcome-based rewards make it difficult to assign credit to intermediate steps. Previous methods mainly focus on creating dense reward signals to guide learning, either through traditional reinforcement learning techniques like inverse reinforcement learning or by using Process Reward Models for step-by-step feedback. In this paper, we identify a fundamental problem in the learning dynamics of LLMs: the magnitude of policy gradients is inherently coupled with the entropy, which leads to inefficient small updates for confident correct actions and potentially destabilizes large updates for uncertain ones. To resolve this, we propose Entropy-Modulated Policy Gradients (EMPG), a framework that re-calibrates the learning signal based on step-wise uncertainty and the final task outcome. EMPG amplifies updates for confident correct actions, penalizes confident errors, and attenuates updates from uncertain steps to stabilize exploration. We further introduce a bonus term for future clarity that encourages agents to find more predictable solution paths. Through comprehensive experiments on three challenging agent tasks, WebShop, ALFWorld, and Deep Search, we demonstrate that EMPG achieves substantial performance gains and significantly outperforms strong policy gradient baselines. Project page is at https://empgseed-seed.github.io/

Many policy optimization approaches in reinforcement learning incorporate a Kullback-Leilbler (KL) divergence to the previous policy, to prevent the policy from changing too quickly. This idea was initially proposed in a seminal paper on Conservative Policy Iteration, with approximations given by algorithms like TRPO and Munchausen Value Iteration (MVI). We continue this line of work by investigating a generalized KL divergence -- called the Tsallis KL divergence -- which use the q-logarithm in the definition. The approach is a strict generalization, as q = 1 corresponds to the standard KL divergence; q > 1 provides a range of new options. We characterize the types of policies learned under the Tsallis KL, and motivate when q >1 could be beneficial. To obtain a practical algorithm that incorporates Tsallis KL regularization, we extend MVI, which is one of the simplest approaches to incorporate KL regularization. We show that this generalized MVI(q) obtains significant improvements over the standard MVI(q = 1) across 35 Atari games.

Soft object manipulation tasks in domestic scenes pose a significant challenge for existing robotic skill learning techniques due to their complex dynamics and variable shape characteristics. Since learning new manipulation skills from human demonstration is an effective way for robot applications, developing prior knowledge of the representation and dynamics of soft objects is necessary. In this regard, we propose a pre-trained soft object manipulation skill learning model, namely SoftGPT, that is trained using large amounts of exploration data, consisting of a three-dimensional heterogeneous graph representation and a GPT-based dynamics model. For each downstream task, a goal-oriented policy agent is trained to predict the subsequent actions, and SoftGPT generates the consequences of these actions. Integrating these two approaches establishes a thinking process in the robot's mind that provides rollout for facilitating policy learning. Our results demonstrate that leveraging prior knowledge through this thinking process can efficiently learn various soft object manipulation skills, with the potential for direct learning from human demonstrations.

Reinforcement learning (RL) promises a framework for near-universal problem-solving. In practice however, RL algorithms are often tailored to specific benchmarks, relying on carefully tuned hyperparameters and algorithmic choices. Recently, powerful model-based RL methods have shown impressive general results across benchmarks but come at the cost of increased complexity and slow run times, limiting their broader applicability. In this paper, we attempt to find a unifying model-free deep RL algorithm that can address a diverse class of domains and problem settings. To achieve this, we leverage model-based representations that approximately linearize the value function, taking advantage of the denser task objectives used by model-based RL while avoiding the costs associated with planning or simulated trajectories. We evaluate our algorithm, MR.Q, on a variety of common RL benchmarks with a single set of hyperparameters and show a competitive performance against domain-specific and general baselines, providing a concrete step towards building general-purpose model-free deep RL algorithms.

Reinforcement learning (RL) is widely used for humanoid control, with on-policy methods such as Proximal Policy Optimization (PPO) enabling robust training via large-scale parallel simulation and, in some cases, zero-shot deployment to real robots. However, the low sample efficiency of on-policy algorithms limits safe adaptation to new environments. Although off-policy RL and model-based RL have shown improved sample efficiency, the gap between large-scale pretraining and efficient finetuning on humanoids still exists. In this paper, we find that off-policy Soft Actor-Critic (SAC), with large-batch update and a high Update-To-Data (UTD) ratio, reliably supports large-scale pretraining of humanoid locomotion policies, achieving zero-shot deployment on real robots. For adaptation, we demonstrate that these SAC-pretrained policies can be finetuned in new environments and out-of-distribution tasks using model-based methods. Data collection in the new environment executes a deterministic policy while stochastic exploration is instead confined to a physics-informed world model. This separation mitigates the risks of random exploration during adaptation while preserving exploratory coverage for improvement. Overall, the approach couples the wall-clock efficiency of large-scale simulation during pretraining with the sample efficiency of model-based learning during fine-tuning.

Reinforcement learning has significantly enhanced the reasoning capabilities of Large Language Models (LLMs) in complex problem-solving tasks. Recently, the introduction of DeepSeek R1 has inspired a surge of interest in leveraging rule-based rewards as a low-cost alternative for computing advantage functions and guiding policy optimization. However, a common challenge observed across many replication and extension efforts is that when multiple sampled responses under a single prompt converge to identical outcomes, whether correct or incorrect, the group-based advantage degenerates to zero. This leads to vanishing gradients and renders the corresponding samples ineffective for learning, ultimately limiting training efficiency and downstream performance. To address this issue, we propose a consistency-aware policy optimization framework that introduces a structured global reward based on outcome consistency, the global loss based on it ensures that, even when model outputs show high intra-group consistency, the training process still receives meaningful learning signals, which encourages the generation of correct and self-consistent reasoning paths from a global perspective. Furthermore, we incorporate an entropy-based soft blending mechanism that adaptively balances local advantage estimation with global optimization, enabling dynamic transitions between exploration and convergence throughout training. Our method introduces several key innovations in both reward design and optimization strategy. We validate its effectiveness through substantial performance gains on multiple mathematical reasoning benchmarks, highlighting the proposed framework's robustness and general applicability. Code of this work has been released at https://github.com/hijih/copo-code.git.

We consider the problem of preference based reinforcement learning (PbRL), where, unlike traditional reinforcement learning, an agent receives feedback only in terms of a 1 bit (0/1) preference over a trajectory pair instead of absolute rewards for them. The success of the traditional RL framework crucially relies on the underlying agent-reward model, which, however, depends on how accurately a system designer can express an appropriate reward function and often a non-trivial task. The main novelty of our framework is the ability to learn from preference-based trajectory feedback that eliminates the need to hand-craft numeric reward models. This paper sets up a formal framework for the PbRL problem with non-markovian rewards, where the trajectory preferences are encoded by a generalized linear model of dimension d. Assuming the transition model is known, we then propose an algorithm with almost optimal regret guarantee of mathcal{O}left( SH d log (T / delta) T right). We further, extend the above algorithm to the case of unknown transition dynamics, and provide an algorithm with near optimal regret guarantee mathcal{O}((d + H^2 + |S|)dT +|mathcal{S||A|TH} ). To the best of our knowledge, our work is one of the first to give tight regret guarantees for preference based RL problems with trajectory preferences.

Reinforcement learning (RL) is typically concerned with estimating stationary policies or single-step models, leveraging the Markov property to factorize problems in time. However, we can also view RL as a generic sequence modeling problem, with the goal being to produce a sequence of actions that leads to a sequence of high rewards. Viewed in this way, it is tempting to consider whether high-capacity sequence prediction models that work well in other domains, such as natural-language processing, can also provide effective solutions to the RL problem. To this end, we explore how RL can be tackled with the tools of sequence modeling, using a Transformer architecture to model distributions over trajectories and repurposing beam search as a planning algorithm. Framing RL as sequence modeling problem simplifies a range of design decisions, allowing us to dispense with many of the components common in offline RL algorithms. We demonstrate the flexibility of this approach across long-horizon dynamics prediction, imitation learning, goal-conditioned RL, and offline RL. Further, we show that this approach can be combined with existing model-free algorithms to yield a state-of-the-art planner in sparse-reward, long-horizon tasks.

In this paper, a unified framework for exploration in reinforcement learning (RL) is proposed based on an option-critic model. The proposed framework learns to integrate a set of diverse exploration strategies so that the agent can adaptively select the most effective exploration strategy over time to realize a relevant exploration-exploitation trade-off for each given task. The effectiveness of the proposed exploration framework is demonstrated by various experiments in the MiniGrid and Atari environments.

From out-competing grandmasters in chess to informing high-stakes healthcare decisions, emerging methods from artificial intelligence are increasingly capable of making complex and strategic decisions in diverse, high-dimensional, and uncertain situations. But can these methods help us devise robust strategies for managing environmental systems under great uncertainty? Here we explore how reinforcement learning, a subfield of artificial intelligence, approaches decision problems through a lens similar to adaptive environmental management: learning through experience to gradually improve decisions with updated knowledge. We review where reinforcement learning (RL) holds promise for improving evidence-informed adaptive management decisions even when classical optimization methods are intractable. For example, model-free deep RL might help identify quantitative decision strategies even when models are nonidentifiable. Finally, we discuss technical and social issues that arise when applying reinforcement learning to adaptive management problems in the environmental domain. Our synthesis suggests that environmental management and computer science can learn from one another about the practices, promises, and perils of experience-based decision-making.

Reinforcement learning (RL) has shown impressive results in sequential decision-making tasks. Meanwhile, Large Language Models (LLMs) and Vision-Language Models (VLMs) have emerged, exhibiting impressive capabilities in multimodal understanding and reasoning. These advances have led to a surge of research integrating LLMs and VLMs into RL. In this survey, we review representative works in which LLMs and VLMs are used to overcome key challenges in RL, such as lack of prior knowledge, long-horizon planning, and reward design. We present a taxonomy that categorizes these LLM/VLM-assisted RL approaches into three roles: agent, planner, and reward. We conclude by exploring open problems, including grounding, bias mitigation, improved representations, and action advice. By consolidating existing research and identifying future directions, this survey establishes a framework for integrating LLMs and VLMs into RL, advancing approaches that unify natural language and visual understanding with sequential decision-making.

Specifying rewards for reinforcement learned (RL) agents is challenging. Preference-based RL (PbRL) mitigates these challenges by inferring a reward from feedback over sets of trajectories. However, the effectiveness of PbRL is limited by the amount of feedback needed to reliably recover the structure of the target reward. We present the PRIor Over Rewards (PRIOR) framework, which incorporates priors about the structure of the reward function and the preference feedback into the reward learning process. Imposing these priors as soft constraints on the reward learning objective reduces the amount of feedback required by half and improves overall reward recovery. Additionally, we demonstrate that using an abstract state space for the computation of the priors further improves the reward learning and the agent's performance.

We provide a theoretical framework for Reinforcement Learning with Human Feedback (RLHF). Our analysis shows that when the true reward function is linear, the widely used maximum likelihood estimator (MLE) converges under both the Bradley-Terry-Luce (BTL) model and the Plackett-Luce (PL) model. However, we show that when training a policy based on the learned reward model, MLE fails while a pessimistic MLE provides policies with improved performance under certain coverage assumptions. Additionally, we demonstrate that under the PL model, the true MLE and an alternative MLE that splits the K-wise comparison into pairwise comparisons both converge. Moreover, the true MLE is asymptotically more efficient. Our results validate the empirical success of existing RLHF algorithms in InstructGPT and provide new insights for algorithm design. Furthermore, our results unify the problem of RLHF and max-entropy Inverse Reinforcement Learning (IRL), and provide the first sample complexity bound for max-entropy IRL.

Soft object manipulation poses significant challenges for robots, requiring effective techniques for state representation and manipulation policy learning. State representation involves capturing the dynamic changes in the environment, while manipulation policy learning focuses on establishing the relationship between robot actions and state transformations to achieve specific goals. To address these challenges, this research paper introduces a novel approach: a dynamic heterogeneous graph-based model for learning goal-oriented soft object manipulation policies. The proposed model utilizes graphs as a unified representation for both states and policy learning. By leveraging the dynamic graph, we can extract crucial information regarding object dynamics and manipulation policies. Furthermore, the model facilitates the integration of demonstrations, enabling guided policy learning. To evaluate the efficacy of our approach, we designed a dough rolling task and conducted experiments using both a differentiable simulator and a real-world humanoid robot. Additionally, several ablation studies were performed to analyze the effect of our method, demonstrating its superiority in achieving human-like behavior.

For continuous action spaces, actor-critic methods are widely used in online reinforcement learning (RL). However, unlike RL algorithms for discrete actions, which generally model the optimal value function using the Bellman optimality operator, RL algorithms for continuous actions typically model Q-values for the current policy using the Bellman operator. These algorithms for continuous actions rely exclusively on policy updates for improvement, which often results in low sample efficiency. This study examines the effectiveness of incorporating the Bellman optimality operator into actor-critic frameworks. Experiments in a simple environment show that modeling optimal values accelerates learning but leads to overestimation bias. To address this, we propose an annealing approach that gradually transitions from the Bellman optimality operator to the Bellman operator, thereby accelerating learning while mitigating bias. Our method, combined with TD3 and SAC, significantly outperforms existing approaches across various locomotion and manipulation tasks, demonstrating improved performance and robustness to hyperparameters related to optimality. The code for this study is available at https://github.com/motokiomura/annealed-q-learning.

Offline reinforcement learning requires reconciling two conflicting aims: learning a policy that improves over the behavior policy that collected the dataset, while at the same time minimizing the deviation from the behavior policy so as to avoid errors due to distributional shift. This trade-off is critical, because most current offline reinforcement learning methods need to query the value of unseen actions during training to improve the policy, and therefore need to either constrain these actions to be in-distribution, or else regularize their values. We propose an offline RL method that never needs to evaluate actions outside of the dataset, but still enables the learned policy to improve substantially over the best behavior in the data through generalization. The main insight in our work is that, instead of evaluating unseen actions from the latest policy, we can approximate the policy improvement step implicitly by treating the state value function as a random variable, with randomness determined by the action (while still integrating over the dynamics to avoid excessive optimism), and then taking a state conditional upper expectile of this random variable to estimate the value of the best actions in that state. This leverages the generalization capacity of the function approximator to estimate the value of the best available action at a given state without ever directly querying a Q-function with this unseen action. Our algorithm alternates between fitting this upper expectile value function and backing it up into a Q-function. Then, we extract the policy via advantage-weighted behavioral cloning. We dub our method implicit Q-learning (IQL). IQL demonstrates the state-of-the-art performance on D4RL, a standard benchmark for offline reinforcement learning. We also demonstrate that IQL achieves strong performance fine-tuning using online interaction after offline initialization.

Reinforcement learning (RL) has enabled machine learning models to achieve significant advances in many fields. Most recently, RL has empowered frontier language models to solve challenging math, science, and coding problems. However, central to any RL algorithm is the reward function, and reward engineering is a notoriously difficult problem in any domain. In this paper, we propose RENT: Reinforcement Learning via Entropy Minimization -- a fully unsupervised RL method that requires no external reward or ground-truth answers, and instead uses the model's entropy of its underlying distribution as an intrinsic reward. We find that by reinforcing the chains of thought that yield high model confidence on its generated answers, the model improves its reasoning ability. In our experiments, we showcase these improvements on an extensive suite of commonly-used reasoning benchmarks, including GSM8K, MATH500, AMC, AIME, and GPQA, and models of varying sizes from the Qwen, Mistral, and Llama families. The generality of our unsupervised learning method lends itself to applicability in a wide range of domains where external supervision is unavailable.

This paper surveys research in the rapidly growing field of enhancing large language models (LLMs) with reinforcement learning (RL), a technique that enables LLMs to improve their performance by receiving feedback in the form of rewards based on the quality of their outputs, allowing them to generate more accurate, coherent, and contextually appropriate responses. In this work, we make a systematic review of the most up-to-date state of knowledge on RL-enhanced LLMs, attempting to consolidate and analyze the rapidly growing research in this field, helping researchers understand the current challenges and advancements. Specifically, we (1) detail the basics of RL; (2) introduce popular RL-enhanced LLMs; (3) review researches on two widely-used reward model-based RL techniques: Reinforcement Learning from Human Feedback (RLHF) and Reinforcement Learning from AI Feedback (RLAIF); and (4) explore Direct Preference Optimization (DPO), a set of methods that bypass the reward model to directly use human preference data for aligning LLM outputs with human expectations. We will also point out current challenges and deficiencies of existing methods and suggest some avenues for further improvements. Project page of this work can be found at: https://github.com/ShuheWang1998/Reinforcement-Learning-Enhanced-LLMs-A-Survey.

Reinforcement learning from Human Feedback (RLHF) learns from preference signals, while standard Reinforcement Learning (RL) directly learns from reward signals. Preferences arguably contain less information than rewards, which makes preference-based RL seemingly more difficult. This paper theoretically proves that, for a wide range of preference models, we can solve preference-based RL directly using existing algorithms and techniques for reward-based RL, with small or no extra costs. Specifically, (1) for preferences that are drawn from reward-based probabilistic models, we reduce the problem to robust reward-based RL that can tolerate small errors in rewards; (2) for general arbitrary preferences where the objective is to find the von Neumann winner, we reduce the problem to multiagent reward-based RL which finds Nash equilibria for factored Markov games under a restricted set of policies. The latter case can be further reduce to adversarial MDP when preferences only depend on the final state. We instantiate all reward-based RL subroutines by concrete provable algorithms, and apply our theory to a large class of models including tabular MDPs and MDPs with generic function approximation. We further provide guarantees when K-wise comparisons are available.

Reinforcement Learning from Human Feedback (RLHF) has emerged as a dominant approach for aligning LLM outputs with human preferences. Inspired by the success of RLHF, we study the performance of multiple algorithms that learn from feedback (Expert Iteration, Proximal Policy Optimization (PPO), Return-Conditioned RL) on improving LLM reasoning capabilities. We investigate both sparse and dense rewards provided to the LLM both heuristically and via a learned reward model. We additionally start from multiple model sizes and initializations both with and without supervised fine-tuning (SFT) data. Overall, we find all algorithms perform comparably, with Expert Iteration performing best in most cases. Surprisingly, we find the sample complexity of Expert Iteration is similar to that of PPO, requiring at most on the order of 10^6 samples to converge from a pretrained checkpoint. We investigate why this is the case, concluding that during RL training models fail to explore significantly beyond solutions already produced by SFT models. Additionally, we discuss a trade off between maj@1 and pass@96 metric performance during SFT training and how conversely RL training improves both simultaneously. We then conclude by discussing the implications of our findings for RLHF and the future role of RL in LLM fine-tuning.

Offline reinforcement learning (RL) aims to learn an optimal policy from pre-collected data. However, it faces challenges of distributional shift, where the learned policy may encounter unseen scenarios not covered in the offline data. Additionally, numerous applications suffer from a scarcity of labeled reward data. Relying on labeled data alone often leads to a narrow state-action distribution, further amplifying the distributional shift, and resulting in suboptimal policy learning. To address these issues, we first recognize that the volume of unlabeled data is typically substantially larger than that of labeled data. We then propose a semi-pessimistic RL method to effectively leverage abundant unlabeled data. Our approach offers several advantages. It considerably simplifies the learning process, as it seeks a lower bound of the reward function, rather than that of the Q-function or state transition function. It is highly flexible, and can be integrated with a range of model-free and model-based RL algorithms. It enjoys the guaranteed improvement when utilizing vast unlabeled data, but requires much less restrictive conditions. We compare our method with a number of alternative solutions, both analytically and numerically, and demonstrate its clear competitiveness. We further illustrate with an application to adaptive deep brain stimulation for Parkinson's disease.

Finding meaningful and accurate dense rewards is a fundamental task in the field of reinforcement learning (RL) that enables agents to explore environments more efficiently. In traditional RL settings, agents learn optimal policies through interactions with an environment guided by reward signals. However, when these signals are sparse, delayed, or poorly aligned with the intended task objectives, agents often struggle to learn effectively. Dense reward functions, which provide informative feedback at every step or state transition, offer a potential solution by shaping agent behavior and accelerating learning. Despite their benefits, poorly crafted reward functions can lead to unintended behaviors, reward hacking, or inefficient exploration. This problem is particularly acute in complex or high-dimensional environments where handcrafted rewards are difficult to specify and validate. To address this, recent research has explored a variety of approaches, including inverse reinforcement learning, reward modeling from human preferences, and self-supervised learning of intrinsic rewards. While these methods offer promising directions, they often involve trade-offs between generality, scalability, and alignment with human intent. This proposal explores several approaches to dealing with these unsolved problems and enhancing the effectiveness and reliability of dense reward construction in different RL applications.

Large pretrained models are showing increasingly better performance in reasoning and planning tasks across different modalities, opening the possibility to leverage them for complex sequential decision making problems. In this paper, we investigate the capabilities of Large Language Models (LLMs) for reinforcement learning (RL) across a diversity of interactive domains. We evaluate their ability to produce decision-making policies, either directly, by generating actions, or indirectly, by first generating reward models to train an agent with RL. Our results show that, even without task-specific fine-tuning, LLMs excel at reward modeling. In particular, crafting rewards through artificial intelligence (AI) feedback yields the most generally applicable approach and can enhance performance by improving credit assignment and exploration. Finally, in environments with unfamiliar dynamics, we explore how fine-tuning LLMs with synthetic data can significantly improve their reward modeling capabilities while mitigating catastrophic forgetting, further broadening their utility in sequential decision-making tasks.

Reinforcement learning (RL) has improved the reasoning abilities of large language models (LLMs), yet state-of-the-art methods still fail to learn on many training problems. On hard problems, on-policy RL rarely explores even a single correct rollout, yielding zero reward and no learning signal for driving improvement. We find that natural solutions to remedy this exploration problem from classical RL, such as entropy bonuses, more permissive clipping of the importance ratio, or direct optimization of pass@k objectives, do not resolve this issue and often destabilize optimization without improving solvability. A natural alternative is to leverage transfer from easier problems. However, we show that mixing easy and hard problems during RL training is counterproductive due to ray interference, where optimization focuses on already-solvable problems in a way that actively inhibits progress on harder ones. To address this challenge, we introduce Privileged On-Policy Exploration (POPE), an approach that leverages human- or other oracle solutions as privileged information to guide exploration on hard problems, unlike methods that use oracle solutions as training targets (e.g., off-policy RL methods or warmstarting from SFT). POPE augments hard problems with prefixes of oracle solutions, enabling RL to obtain non-zero rewards during guided rollouts. Crucially, the resulting behaviors transfer back to the original, unguided problems through a synergy between instruction-following and reasoning. Empirically, POPE expands the set of solvable problems and substantially improves performance on challenging reasoning benchmarks.

We study a class of reinforcement learning problems where the reward signals for policy learning are generated by a discriminator that is dependent on and jointly optimized with the policy. This interdependence between the policy and the discriminator leads to an unstable learning process because reward signals from an immature discriminator are noisy and impede policy learning, and conversely, an untrained policy impedes discriminator learning. We call this learning setting Internally Rewarded Reinforcement Learning (IRRL) as the reward is not provided directly by the environment but internally by the discriminator. In this paper, we formally formulate IRRL and present a class of problems that belong to IRRL. We theoretically derive and empirically analyze the effect of the reward function in IRRL and based on these analyses propose the clipped linear reward function. Experimental results show that the proposed reward function can consistently stabilize the training process by reducing the impact of reward noise, which leads to faster convergence and higher performance compared with baselines in diverse tasks.

Reinforcement learning (RL) plays a crucial role in shaping the behavior of large language and reasoning models (LLMs/LRMs). However, it often produces brittle and unstable policies, leading to critical failures such as spurious reasoning, deceptive alignment, and instruction disobedience that undermine the trustworthiness and safety of LLMs/LRMs. Currently, these issues lack a unified theoretical explanation and are typically addressed using ad-hoc heuristics. This paper presents a rigorous mathematical framework for analyzing the stability of the mapping from a reward function to the optimal policy. We show that policy brittleness often stems from non-unique optimal actions, a common occurrence when multiple valid traces exist in a reasoning task. This theoretical lens provides a unified explanation for a range of seemingly disparate failures, reframing them as rational outcomes of optimizing rewards that may be incomplete or noisy, especially in the presence of action degeneracy. We extend this analysis from the fundamental single-reward setting to the more realistic multi-reward RL across diverse domains, showing how stability is governed by an "effective reward" aggregation mechanism. We also prove that entropy regularization restores policy stability at the cost of increased stochasticity. Our framework provides a unified explanation for recent empirical findings on deceptive reasoning, instruction-following trade-offs, and RLHF-induced sophistry, and is further validated through perturbation experiments in multi-reward RL. This work advances policy-stability analysis from empirical heuristics towards a principled theory, offering essential insights for designing safer and more trustworthy AI systems.

Policy gradient algorithms have been successfully applied to enhance the reasoning capabilities of large language models (LLMs). Despite the widespread use of Kullback-Leibler (KL) regularization in policy gradient algorithms to stabilize training, the systematic exploration of how different KL divergence formulations can be estimated and integrated into surrogate loss functions for online reinforcement learning (RL) presents a nuanced and systematically explorable design space. In this paper, we propose regularized policy gradient (RPG), a systematic framework for deriving and analyzing KL-regularized policy gradient methods in the online RL setting. We derive policy gradients and corresponding surrogate loss functions for objectives regularized by both forward and reverse KL divergences, considering both normalized and unnormalized policy distributions. Furthermore, we present derivations for fully differentiable loss functions as well as REINFORCE-style gradient estimators, accommodating diverse algorithmic needs. We conduct extensive experiments on RL for LLM reasoning using these methods, showing improved or competitive results in terms of training stability and performance compared to strong baselines such as GRPO, REINFORCE++, and DAPO. The code is available at https://github.com/complex-reasoning/RPG.

The success of AI assistants based on language models (LLMs) hinges crucially on Reinforcement Learning from Human Feedback (RLHF), which enables the generation of responses more aligned with human preferences. As universal AI assistants, there's a growing expectation for them to perform consistently across various domains. However, previous work shows that Reinforcement Learning (RL) often exploits shortcuts to attain high rewards and overlooks challenging samples. This focus on quick reward gains undermines both the stability in training and the model's ability to generalize to new, unseen data. In this work, we propose a novel approach that can learn a consistent policy via RL across various data groups or domains. Given the challenges associated with acquiring group annotations, our method automatically classifies data into different groups, deliberately maximizing performance variance. Then, we optimize the policy to perform well on challenging groups. Lastly, leveraging the established groups, our approach adaptively adjusts the exploration space, allocating more learning capacity to more challenging data and preventing the model from over-optimizing on simpler data. Experimental results indicate that our approach significantly enhances training stability and model generalization.

Typical reinforcement learning (RL) methods for LLM reasoning waste compute on hard problems, where correct on-policy traces are rare, policy gradients vanish, and learning stalls. To bootstrap more efficient RL, we consider reusing old sampling FLOPs (from prior inference or RL training) in the form of off-policy traces. Standard off-policy methods supervise against off-policy data, causing instabilities during RL optimization. We introduce PrefixRL, where we condition on the prefix of successful off-policy traces and run on-policy RL to complete them, side-stepping off-policy instabilities. PrefixRL boosts the learning signal on hard problems by modulating the difficulty of the problem through the off-policy prefix length. We prove that the PrefixRL objective is not only consistent with the standard RL objective but also more sample efficient. Empirically, we discover back-generalization: training only on prefixed problems generalizes to out-of-distribution unprefixed performance, with learned strategies often differing from those in the prefix. In our experiments, we source the off-policy traces by rejection sampling with the base model, creating a self-improvement loop. On hard reasoning problems, PrefixRL reaches the same training reward 2x faster than the strongest baseline (SFT on off-policy data then RL), even after accounting for the compute spent on the initial rejection sampling, and increases the final reward by 3x. The gains transfer to held-out benchmarks, and PrefixRL is still effective when off-policy traces are derived from a different model family, validating its flexibility in practical settings.

We introduce Prompt Curriculum Learning (PCL), a lightweight reinforcement learning (RL) algorithm that selects intermediate-difficulty prompts using a learned value model to post-train language models. Since post-training LLMs via RL remains sensitive to batching and prompt selection strategies, we first conduct a series of systematic experiments where we (1) determine the optimal training batch size that balances generation efficiency and gradient quality and (2) establish the importance of focusing on prompts of intermediate difficulty for the policy. We build upon these results to design PCL, which identifies prompts of intermediate difficulty for the current policy in an on-policy manner by using a value model that is concurrently updated based on the current policy. By focusing on informative prompts that yield high effective ratios, PCL achieves either the highest performance or requires significantly less time to reach comparable performance to its counterparts. Compared to rollout-based filtering methods, PCL avoids costly rollouts and achieves 12.1times and 16.9times faster speed on identifying intermediate-difficulty prompts when training on MATH and DeepScaleR, respectively. We further demonstrate that our value model accurately predicts prompt difficulty and allows PCL to focus on progressively more challenging prompts during RL. Our results present a new methodology that delivers improved tradeoff between upper-bound performance and efficiency for reasoning-focused RL.

As autonomous agents become adept at understanding and interacting with graphical user interface (GUI) environments, a new era of automated task execution is emerging. Recent studies have demonstrated that Reinforcement Learning (RL) can effectively enhance agents' performance in dynamic interactive GUI environments. However, these methods face two key limitations: (1) they overlook the significant variation in difficulty across different GUI tasks by treating the entire training data as a uniform set, which hampers the agent's ability to adapt its learning process; and (2) most approaches collapse task-specific nuances into a single, coarse reward, leaving the agent with a uniform signal that yields inefficient policy updates. To address these limitations, we propose CRAFT-GUI, a curriculum learning framework based on Group Relative Policy Optimization (GRPO) that explicitly accounts for the varying difficulty across trajectories. To enable more fine-grained policy optimization, we design a reward function that combines simple rule-based signals with model-judged evaluation, providing richer and more nuanced feedback during training. Experimental results demonstrate that our method achieves significant improvements over previous state-of-the-art approaches, outperforming them by 5.6% on public benchmarks Android Control and 10.3% on our internal online benchmarks, respectively. These findings empirically validate the effectiveness of integrating reinforcement learning with curriculum learning in GUI interaction tasks.

In recent years, Reinforcement Learning (RL) has been applied to real-world problems with increasing success. Such applications often require to put constraints on the agent's behavior. Existing algorithms for constrained RL (CRL) rely on gradient descent-ascent, but this approach comes with a caveat. While these algorithms are guaranteed to converge on average, they do not guarantee last-iterate convergence, i.e., the current policy of the agent may never converge to the optimal solution. In practice, it is often observed that the policy alternates between satisfying the constraints and maximizing the reward, rarely accomplishing both objectives simultaneously. Here, we address this problem by introducing Reinforcement Learning with Optimistic Ascent-Descent (ReLOAD), a principled CRL method with guaranteed last-iterate convergence. We demonstrate its empirical effectiveness on a wide variety of CRL problems including discrete MDPs and continuous control. In the process we establish a benchmark of challenging CRL problems.

Reinforcement learning (RL) has emerged as a promising strategy for finetuning small language models (SLMs) to solve targeted tasks such as math and coding. However, RL algorithms tend to be resource-intensive, taking a significant amount of time to train. We propose RAPID, a novel RL algorithm that can substantially reduce the running time of RL. Our key insight is that RL tends to be costly due to the need to perform both inference and backpropagation during training. To maximize use of computational resources, our algorithm performs inference in large batches, and then performs off-policy policy gradient updates in mini-batches. For off-policy updates, we incorporate group advantage estimation into the policy gradient algorithm, and derive an importance weighted estimator to correct for the bias arising from off-policy learning. Our experiments demonstrate that our algorithm can reduce running time by 11%-34% on three benchmarks compared to state-of-the-art RL algorithms while maintaining similar or better accuracy.

Reinforcement learning (RL) is the dominant paradigm for sharpening strategic tool use capabilities of LLMs on long-horizon, sparsely-rewarded agent tasks, yet it faces a fundamental challenge of exploration-exploitation trade-off. Existing studies stimulate exploration through the lens of policy entropy, but such mechanical entropy maximization is prone to RL training instability due to the multi-turn distribution shifting. In this paper, we target the progressive exploration-exploitation balance under the guidance of the agent own experiences without succumbing to either entropy collapsing or runaway divergence. We propose SPEAR, a curriculum-based self-imitation learning (SIL) recipe for training agentic LLMs. It extends the vanilla SIL framework, where a replay buffer stores self-generated promising trajectories for off-policy update, by gradually steering the policy evolution within a well-balanced range of entropy across stages. Specifically, our approach incorporates a curriculum to manage the exploration process, utilizing intrinsic rewards to foster skill-level exploration and facilitating action-level exploration through SIL. At first, the auxiliary tool call reward plays a critical role in the accumulation of tool-use skills, enabling broad exposure to the unfamiliar distributions of the environment feedback with an upward entropy trend. As training progresses, self-imitation gets strengthened to exploit existing successful patterns from replayed experiences for comparative action-level exploration, accelerating solution iteration without unbounded entropy growth. To further stabilize training, we recalibrate the advantages of experiences in the replay buffer to address the potential policy drift. Reugularizations such as the clipping of tokens with high covariance between probability and advantage are introduced to the trajectory-level entropy control to curb over-confidence.

Training LLM agents in multi-turn environments with sparse rewards, where completing a single task requires 30+ turns of interaction within an episode, presents a fundamental challenge for reinforcement learning. We identify a critical failure mode unique to this setting: the exploration-exploitation cascade failure. This cascade begins with early-stage policy premature convergence, where sparse feedback causes agents to commit to flawed, low-entropy strategies. Subsequently, agents enter late-stage policy collapse, where conventional entropy regularization becomes counterproductive, promoting chaotic exploration that destabilizes training. We propose Entropy-regularized Policy Optimization (EPO), a general framework that breaks this failure cycle through three synergistic mechanisms: (1) adopting entropy regularization in multi-turn settings to enhance exploration, (2) an entropy smoothing regularizer that bounds policy entropy within historical averages to prevent abrupt fluctuations, and (3) adaptive phase-based weighting that balances exploration and exploitation across training. Our analysis justifies that EPO guarantees monotonically decreasing entropy variance while maintaining convergence. EPO achieves up to 152% performance improvement on ScienceWorld and up to 19.8% on ALFWorld. Our work demonstrates that multi-turn sparse-reward settings require fundamentally different entropy control than traditional RL, with broad implications for LLM agent training.

In Reinforcement Learning (RL), regularization has emerged as a popular tool both in theory and practice, typically based either on an entropy bonus or a Kullback-Leibler divergence that constrains successive policies. In practice, these approaches have been shown to improve exploration, robustness and stability, giving rise to popular Deep RL algorithms such as SAC and TRPO. Policy Mirror Descent (PMD) is a theoretical framework that solves this general regularized policy optimization problem, however the closed-form solution involves the sum of all past Q-functions, which is intractable in practice. We propose and analyze PMD-like algorithms that only keep the last M Q-functions in memory, and show that for finite and large enough M, a convergent algorithm can be derived, introducing no error in the policy update, unlike prior deep RL PMD implementations. StaQ, the resulting algorithm, enjoys strong theoretical guarantees and is competitive with deep RL baselines, while exhibiting less performance oscillation, paving the way for fully stable deep RL algorithms and providing a testbed for experimentation with Policy Mirror Descent.

Large Language Models (LLMs) are increasingly being explored for building Agents capable of active environmental interaction (e.g., via tool use) to solve complex problems. Reinforcement Learning (RL) is considered a key technology with significant potential for training such Agents; however, the effective application of RL to LLM Agents is still in its nascent stages and faces considerable challenges. Currently, this emerging field lacks in-depth exploration into RL approaches specifically tailored for the LLM Agent context, alongside a scarcity of flexible and easily extensible training frameworks designed for this purpose. To help advance this area, this paper first revisits and clarifies Reinforcement Learning methodologies for LLM Agents by systematically extending the Markov Decision Process (MDP) framework to comprehensively define the key components of an LLM Agent. Secondly, we introduce Agent-R1, a modular, flexible, and user-friendly training framework for RL-based LLM Agents, designed for straightforward adaptation across diverse task scenarios and interactive environments. We conducted experiments on Multihop QA benchmark tasks, providing initial validation for the effectiveness of our proposed methods and framework.

Reinforcement learning (RL) is rapidly reaching and surpassing human-level control capabilities. However, state-of-the-art RL algorithms often require timesteps and reaction times significantly faster than human capabilities, which is impractical in real-world settings and typically necessitates specialized hardware. Such speeds are difficult to achieve in the real world and often requires specialized hardware. We introduce Sequence Reinforcement Learning (SRL), an RL algorithm designed to produce a sequence of actions for a given input state, enabling effective control at lower decision frequencies. SRL addresses the challenges of learning action sequences by employing both a model and an actor-critic architecture operating at different temporal scales. We propose a "temporal recall" mechanism, where the critic uses the model to estimate intermediate states between primitive actions, providing a learning signal for each individual action within the sequence. Once training is complete, the actor can generate action sequences independently of the model, achieving model-free control at a slower frequency. We evaluate SRL on a suite of continuous control tasks, demonstrating that it achieves performance comparable to state-of-the-art algorithms while significantly reducing actor sample complexity. To better assess performance across varying decision frequencies, we introduce the Frequency-Averaged Score (FAS) metric. Our results show that SRL significantly outperforms traditional RL algorithms in terms of FAS, making it particularly suitable for applications requiring variable decision frequencies. Additionally, we compare SRL with model-based online planning, showing that SRL achieves superior FAS while leveraging the same model during training that online planners use for planning.

Reinforcement learning (RL) post-training is crucial for LLM alignment and reasoning, but existing policy-based methods, such as PPO and DPO, can fall short of fixing shortcuts inherited from pre-training. In this work, we introduce Qsharp, a value-based algorithm for KL-regularized RL that guides the reference policy using the optimal regularized Q function. We propose to learn the optimal Q function using distributional RL on an aggregated online dataset. Unlike prior value-based baselines that guide the model using unregularized Q-values, our method is theoretically principled and provably learns the optimal policy for the KL-regularized RL problem. Empirically, Qsharp outperforms prior baselines in math reasoning benchmarks while maintaining a smaller KL divergence to the reference policy. Theoretically, we establish a reduction from KL-regularized RL to no-regret online learning, providing the first bounds for deterministic MDPs under only realizability. Thanks to distributional RL, our bounds are also variance-dependent and converge faster when the reference policy has small variance. In sum, our results highlight Qsharp as an effective approach for post-training LLMs, offering both improved performance and theoretical guarantees. The code can be found at https://github.com/jinpz/q_sharp.

The framework of reinforcement learning or optimal control provides a mathematical formalization of intelligent decision making that is powerful and broadly applicable. While the general form of the reinforcement learning problem enables effective reasoning about uncertainty, the connection between reinforcement learning and inference in probabilistic models is not immediately obvious. However, such a connection has considerable value when it comes to algorithm design: formalizing a problem as probabilistic inference in principle allows us to bring to bear a wide array of approximate inference tools, extend the model in flexible and powerful ways, and reason about compositionality and partial observability. In this article, we will discuss how a generalization of the reinforcement learning or optimal control problem, which is sometimes termed maximum entropy reinforcement learning, is equivalent to exact probabilistic inference in the case of deterministic dynamics, and variational inference in the case of stochastic dynamics. We will present a detailed derivation of this framework, overview prior work that has drawn on this and related ideas to propose new reinforcement learning and control algorithms, and describe perspectives on future research.

Off-policy reinforcement learning (RL) has proven to be a powerful framework for guiding agents' actions in environments with stochastic rewards and unknown or noisy state dynamics. In many real-world settings, these agents must operate in multiple environments, each with slightly different dynamics. For example, we may be interested in developing policies to guide medical treatment for patients with and without a given disease, or policies to navigate curriculum design for students with and without a learning disability. Here, we introduce nested policy fitted Q-iteration (NFQI), an RL framework that finds optimal policies in environments that exhibit such a structure. Our approach develops a nested Q-value function that takes advantage of the shared structure between two groups of observations from two separate environments while allowing their policies to be distinct from one another. We find that NFQI yields policies that rely on relevant features and perform at least as well as a policy that does not consider group structure. We demonstrate NFQI's performance using an OpenAI Gym environment and a clinical decision making RL task. Our results suggest that NFQI can develop policies that are better suited to many real-world clinical environments.