Policy Learning

Zero-shot Transfer in Reinforcement Learning (RL) aims to train an agent that can generate optimal policies for any reward function, without additional learning at transfer time, while training only on reward-free trajectories. For their generality over tasks, such models are sometimes called ``Behavioral Foundation Models'' (BFMs). While they have shown strong performances and improvements in recent years, the current framework and algorithms still assume that, during the transfer phase, the agent is informed offline about the reward (the task to solve) through a dataset of state-reward pairs, which it uses to pick the best policy to deploy. However, in practice if the reward is a black-box (e.g. direct user feedback), it is not possible to generate such a dataset: it is necessary to observe the reward through interactions with the environment. In other words, the current framework of offline transfer is not aligned with the traditional RL setting of online learning through trial-and-error, which requires exploration in order to find rewards. This paper proposes to tackle this new online transfer in zero-shot RL, with the key insight that the BFM itself can be used to generate exploration policies. We show that it is possible to frame this online learning problem in terms of a bandit-like exploration-exploitation problem. More precisely, at each step the bandit algorithm recommends a policy, the BFM executes it in the environment, which yields a reward and a new state; we repeat the process until we converge to the optimal policy. In the popular context of linear reward approximation, we derive a formulation inspired by Upper Confidence Bound and show that exploration can be achieved through the minimization of the eigenvalues of an uncertainty matrix. We evaluate qualitatively and quantitatively our framework on a simple environment to validate the concept of our method.

Real-world robot learning increasingly relies on heterogeneous data, but demonstrations and rollouts often mix useful progress with stalls, corrections, and suboptimal behavior. Effective policy learning therefore requires frame-level advantages that distinguish reliable local progress from failures and regressions. We propose \textbf{S}elf-supervised \textbf{T}emporal \textbf{E}nsemble \textbf{A}dvantage \textbf{M}odeling (\textbf{STEAM}), a label-free method that learns such advantages from expert demonstrations. STEAM trains an ensemble of temporal-offset predictors on frame pairs within expert trajectories, using the normalized temporal offset between two frames as a self-supervised signal. Each predictor maps a frame pair to a distribution over temporal offsets, which is converted into a scalar advantage. STEAM then takes the minimum advantage across the ensemble to score mixed-quality rollout data conservatively. Across real-world bimanual towel folding, chip checkout, table clearing, and cola restocking tasks, STEAM identifies stalls, failures, and recoveries. When combined with CFGRL, STEAM achieves the highest policy success rate on all four tasks, averaging $83.5\%$ against $58.8\%$ for the best baseline. Project page: https://rlinf.github.io/steam/.

Behavior-cloned policies often learn multiple behavior modes from demonstration datasets, including modes that are unsafe or otherwise undesired at deployment. For example, a policy trained on diverse handover demonstrations may learn to pass a knife blade-first. Standard remedies such as data curation and inference-time steering either require access to the original demonstrations for full retraining or add substantial inference-time overhead. To address this gap, we propose MoRE(Mode Redirection), which redirects policy rollouts toward desired behavior modes through a short "uncloning" step. Specifically, MoRE distills the redirection signal from a temporary mode classifier into the policy weights to steer behavior. A retain loss balances this edit by preserving desired-mode competence, allowing the standalone policy to suppress unwanted modes with zero inference-time overhead. Across eight simulated and real-world tasks, MoRE improves the average deployment success rate (SR) by 44 percentage points over the original mixed-mode policy. Among all compared adaptation and steering baselines, MoRE achieves the strongest SR and approaches the filtered-data retraining reference, while preserving task competence and inference speed. MoRE also generalizes across robot policy backbones, including Diffusion Policy and the Pi0.5 VLA, diverse task categories, and real-world deployments.

We propose KL-Coupled Policy Regularization (KCPR), a policy coordination framework for Reward-Punishment Reinforcement Learning (RPRL). Based on KCPR, we derive KL-Coupled Soft Optimality (KCSO) and develop its deep realization, klDMP. Unlike existing RPRL approaches that optimize reward-seeking and punishment-related policies largely independently, KCPR enables direct interactions between companion policies by treating each as a dynamically learned prior for the other. KCSO yields coupled soft-optimal policies and KL-regularized Bellman operators, allowing reward and punishment information to jointly influence value propagation. To improve learning stability, we introduce a companion-prior softening mechanism and evaluate separate replay-buffer designs for balancing reward- and punishment-related experience. Experiments in grid-world and Gazebo robotic navigation tasks demonstrate that klDMP improves safety and learning stability while maintaining competitive task performance compared with DQN, SQL and softDMP. These results suggest that policy-level coordination provides an effective mechanism for integrating multiple behavioral objectives and may serve as a useful design principle for reinforcement learning systems with interacting motivational processes.

Robots deployed in the real world rarely operate under a single fixed dynamics model: wind changes, payloads vary, batteries drain, contacts shift, and hardware wears. Yet most learning-based controllers are trained once and deployed as if learning were complete. This prevents the robot from using deployment experience to further improve task performance. In this work, we propose a continual learning framework that uses real-world experience to improve robot policies under hidden and recurring dynamics. Our method learns a condition-aware dynamics model from real state-action trajectories by combining an analytical physics prior with a neural residual for unmodeled effects. A recurrent encoder infers the current hidden condition from recent interaction, and this estimate conditions both the residual model and the policy. Policy learning is performed via differentiable simulation using diverse learned dynamics sampled from the latent model. At deployment, these sampled conditions are replaced by conditions inferred online from recent real interaction, allowing the policy to recover recurring dynamics by recognition rather than residual re-fitting. Through extensive simulation studies and real-world experiments, we demonstrate that the framework improves policy performance under diverse unobserved disturbances. On real quadrotor trajectory tracking under changing wind, the policy recovers from recurring disturbances in roughly 1s, about 5x faster than online residual re-fitting. It also reduces large-disturbance hover and tracking errors by 65.7% and 53.3% over the state-of-the-art online adaptation approaches

Sparse rewards are inherently challenging for reinforcement learning agents as they lack intermediate feedback to guide exploration and to correctly attribute the sparse success rewards to relevant parts of the trajectory. Naive reward shaping can induce reward hacking, yielding policies that exploit auxiliary signals instead of solving the intended task. Potential-based reward shaping (PBRS) guarantees preservation of the optimal policy set, but requires the definition of a heuristic potential function over the state space. In this work, we introduce the VLM-guided PBRS framework VLM-PBRS that learns the potential function directly from vision language model (VLM) feedback. We query a lightweight VLM to obtain preferences over image pairs and train a model of the potential function using these preferences. As this approach is based on potential-based reward shaping, it preserves the original optimal policies, and removes the need for expert-designed reward shaping terms. Because large VLMs are prohibitively expensive to invoke repeatedly during policy learning, we employ smaller, more computationally efficient VLMs. Although the resulting preference labels are less accurate, empirical evidence shows that the preference labels can still be used to accelerate learning. We validate our method empirically in the Meta-World and Franka Kitchen environments and highlight the connection between VLM preference label accuracy and sample efficiency improvements. Our contributions are threefold: (1) the first application of VLM preference-based learning to synthesize a potential function for PBRS, (2) a principled, low-cost solution that leverages small VLMs, and (3) extensive empirical demonstration of improved sample efficiency and robustness to reward hacking.

For LLM agents in multi-step interactive environments, a key challenge is to make effective use of accumulated interaction experience. Existing work has typically separated two uses of such experience: keeping it outside the model as natural-language rules for later prompting, or using trajectories and feedback to update the model parameters. The former is easy to interpret but can fall out of sync with the evolving policy; the latter improves the policy more broadly but provides only limited correction for local mistakes in sparse-reward settings. We present Joint Learning of Experiential Rules and Policies for LLM Agents (JERP), which updates a long-term experiential-rule pool and the policy from the same interaction trajectories. At decision time, JERP retrieves task-relevant rules and conditions the agent on them together with the interaction history. After each episode, it uses the collected trajectories both to optimize the policy and to revise the rule pool by comparing current rollouts with reference successful trajectories. This coupling keeps the rule pool aligned with the evolving policy while allowing stable and effective behaviors to be gradually absorbed into the model itself. Experiments on AlfWorld and WebShop show that JERP yields consistent gains in decision performance for complex interactive tasks.

Outcome-based reinforcement learning provides a stable optimization backbone for language agents, but its sparse trajectory-level rewards provide little guidance on which intermediate decisions should be reinforced or suppressed. On-policy self-distillation offers dense token-level supervision, yet existing skill-conditioned variants often rely on external skill memories or retrieved privileged context, which are costly to maintain and can be mismatched with the state distribution induced by the current policy in multi-turn interaction. We propose \textbf{OPID} (\textbf{O}n-\textbf{P}olicy Sk\textbf{i}ll \textbf{D}istillation), a framework that extracts skill supervision directly from completed on-policy trajectories. OPID represents trajectory hindsight as hierarchical skills: episode-level skills capture global workflows or failure-avoidance rules, while step-level skills capture local decision knowledge at critical timesteps. A critical-first routing mechanism uses step-level skills when critical decisions are identified and falls back to episode-level skills as default guidance otherwise. The selected skill is injected into the interaction history, allowing the old policy to re-score the same sampled response under both original and skill-augmented contexts. The resulting log-probability shift yields a token-level self-distillation advantage, which is combined with the outcome advantage for policy optimization. OPID thus preserves RL as the primary training objective while introducing dense, distribution-matched hindsight supervision. Experiments on ALFWorld, WebShop and Search-based QA demonstrate that OPID generally improves agent performance, sample efficiency, and robustness over outcome-only RL and existing skill-distillation baselines. Our code is available at https://github.com/jinyangwu/OPID/tree/main.

Deliberating takes time. In real-time settings, that time is not free. Standard reinforcement learning (RL) sidesteps this as the environment waits indefinitely for the agent's decision. Instead, we study real-time RL environments where the environment progresses while waiting for the agent's action. Building on prior real-time formalizations, we introduce variable-delay real-time RL, where the agent chooses how long to deliberate at each decision point since the environment progresses. For the planning agents we use, the right delay is state-dependent, and naively planning how long to plan can paralyze the agent. We instead approach this setting by training a lightweight gating policy on top of a planner to select state-dependent planning budgets. Across real-time Pac-Man, Tetris, Snake, Speed Hex, and Speed Go, our gating policy outperforms fixed-budget and heuristic baselines, and transfers to a real-time setup where the environment and agent run on two different GPUs.

In actor-critic reinforcement learning, network architectures are typically manually designed. Automating this design is challenging because each candidate must be trained before evaluation, and the design space is open-ended. To address these challenges, we introduce EVOM, an agentic meta-evolution framework for discovering high-performance actor-critic architectures. We frame architecture search as a bi-level optimization: an inner loop trains weights via the low-fidelity proximal policy optimization (PPO), while an outer loop drives meta-evolution by iteratively refining architecture programs. Crucially, this outer loop is powered by an LLM-based design agent that operates purely as an architecture designer, completely decoupled from policy execution and environment control. Experiments reveal that EVOM outperforms the manually designed baseline, an LLM-guided random search, and the state-of-the-art LLM-guided programmatic policy search method MLES, delivering superior performance on Ant-v4 and HalfCheetah-v4. Ablation studies validate that both the meta-evolution loop and the LLM Design Agent are indispensable for final performance.

When fine-tuning Large Language Models (LLMs), there has been success in minimizing both memory usage and computation with Parameter-Efficient Fine-Tuning (PEFT), like Low Rank Adaptation (LoRA). In this article, we have explored whether this approach is transferable to the world of robotics and Reinforcement Learning (RL), allowing learning with reduced memory usage and improved computational performance. Specifically, we focused on a version of multi-task robotics, where a library of specialist policies are created. In such a library memory efficiency is especially important. We used a Proximal Policy Optimization (PPO) algorithm and fine-tuned a baseline model to different tasks using LoRA. Our results demonstrate that, depending on the hyperparameters, LoRA can minimize memory usage by a factor of 20-160 compared to full fine-tuning of all layers. This implies a 90-95% storage saving when deploying a library of many (10-50) specialized policies, which can be the differentiating factor between being able to store the entire library in memory or having to use swap-memory in an applied robotics setting. At the same time, our results indicate that there is no significant difference in the success-rate between full fine-tuning and LoRA fine-tuning for the selected tasks.

We study optimal-policy geometry in structured Markov decision processes. While approximate dynamic programming and reinforcement learning typically approximate high-dimensional value functions, we show that optimal policies induce simpler decision tessellations. We propose boundary-based policy approximations that learn policy regions directly. A policy-loss decomposition links performance degradation to action margins and explains why errors concentrate near indifference boundaries. Inventory control and queue admission experiments show lower policy error, smaller value gaps, faster error decay, and stability than reinforcement learning baselines.

Reward design remains a major bottleneck in reinforcement learning for robot locomotion, where successful policies often depend on carefully tuned, task-specific reward functions. Preference-based reinforcement learning offers an alternative, but existing LLM-based methods typically ask for a single overall judgment between behaviors, making it difficult to capture the multiple competing objectives that underlie high-quality locomotion. We present Multi-Objective AI-Informed Preference Learning (MAPL), a framework that learns locomotion rewards from high-level natural language objectives rather than manually engineered reward equations. MAPL prompts a large language model to compare trajectories independently along semantically meaningful criteria, using generic language descriptions that are terrain-invariant and require little domain expertise. These objective-wise preferences are used to train a multi-head preference scoring model, whose outputs are aggregated to form a scalar reward for policy optimization. Across four quadruped locomotion environments, MAPL trains policies using only LLM-generated preferences and achieves performance comparable to or better than expert-designed rewards, while eliminating task-specific reward engineering.

Learning effective policies for adaptive data acquisition remains challenging: posterior-based methods rely on surrogate models and posterior approximations that can be misspecified or biased, while direct policy-learning methods map from historical observations and fail to exploit available model representations, making learning harder. We introduce policy learning with belief representations (POLAR), based on the insight that optimal data acquisition depends on the observation history only through a sufficient belief state. Specifically, POLAR decouples representation learning from policy learning by leveraging pretrained predictive foundation models as belief-state encoders, training a policy head on top of their representations. This yields a simple, unified amortised policy learning framework for Bayesian experimental design, Bayesian optimisation, and active learning, differing only in the task-specific utility used to train the policy. Empirically, we find that POLAR outperforms state-of-the-art amortised methods across diverse tasks while requiring far fewer training samples, demonstrating a significant step in the scalability and efficiency of amortised data acquisition.

We introduce a PAC framework in which the learner can access sampling oracles both before and at decision time. Sample complexity is measured by a pair $(n,m)$, where $n$ is the learning budget spent before a query is known and $m$ is the additional sampling budget per query. We demonstrate its relevance in discounted Markov decision processes with exogenous i.i.d.\ contexts revealed before acting. Contexts may affect both rewards and transitions but remain uncontrolled by the agent. The learner can sample the unknown context distribution and the transition kernel. We study policy evaluation (PE), best-value estimation (BVE), and best-policy extraction (BPE). When rewards and transitions are known, a variance-reduced algorithm solves all three tasks with sample complexity $\bigl(\widetilde O((1-γ)^{-3}\varepsilon^{-2}),0\bigr)$, which is minimax optimal up to logarithmic factors. Let $\mathcal{X}$ be the controlled state space. When transitions are also unknown, we give a PE algorithm with complexity $\bigl(\widetilde O(|\mathcal X|(1-γ)^{-3}\varepsilon^{-2}), \widetilde O((1-γ)^{-2}\varepsilon^{-2})\bigr)$ and matching lower bounds at this budget pair. For BVE and BPE, we give an algorithm with a common offline budget $\widetilde O(|\mathcal X|^2|\mathcal A|(1-γ)^{-4}\varepsilon^{-2})$ and respective query costs $\widetilde O(|\mathcal A|(1-γ)^{-2}\varepsilon^{-2})$ and $\widetilde O(|\mathcal A|(1-γ)^{-3}\varepsilon^{-2})$. Importantly, all bounds are independent of the context-space cardinality.

Many reinforcement learning (RL) problems in the infinite-horizon average-reward setting require optimizing multiple conflicting objectives while satisfying multiple safety constraints. A common approach is concave scalarization, where the agent maximizes a utility $f(J^π_{r_1}, \ldots, J^π_{r_M})$ subject to a scalarized constraint $g(J^π_{c_1}, \ldots, J^π_{c_N}) \ge 0$, where $J^π_{r_m}$ and $J^π_{c_n}$ denote the average-reward and cost under policy $π$. However, the nonlinearity of $f$ and $g$ introduces bias in policy-gradient and actor-critic methods, since gradients must be evaluated using noisy estimates of $J^π,$ and $\mathbb{E}[\partial f(J^π)] \neq \partial f(\mathbb{E}[J^π]),$ and this bias propagates through both primal and dual updates. We propose an MLMC-based primal-dual Natural Actor-Critic algorithm for average-reward MDPs that controls bias in scalarized objectives, constraint evaluation, and actor-critic estimation without requiring mixing-time knowledge. We show that the algorithm achieves optimal global convergence and constraint-violation rates of $\tilde{O}(1/\sqrt{T})$. To our knowledge, this is the first result establishing optimal convergence for concave scalarized multi-objective RL in the average-reward setting, both with and without constraints, and the first to do so without mixing-time information even in the absence of scalarization.

Reinforcement Learning with Verifiable Rewards (RLVR) for language-model reasoning can fail at both extremes of task difficulty: easy prompts often produce all-correct, low-diversity rollout groups with little gradient signal, while hard prompts can produce all-incorrect groups with no positive reward. We introduce ExTra (Exploratory Trajectory Optimization), a GRPO-compatible framework that extracts exploration signals from the model's own rollouts. ExTra combines two mechanisms: (i) a novelty reward that adds embedding-based diversity bonuses after GRPO normalization, rewarding diverse correct solutions; and (ii) entropy-guided prefix regeneration, which scores partial trajectories using entropy signals and continues exploration from promising intermediate steps. Across six mathematical reasoning benchmarks, ExTra improves Qwen3-1.7B over GRPO by about +5 points on pass@1 and +7 points on pass@16, showing that trajectory-level exploration signals can improve both single-sample accuracy and inference-time coverage.

Large language models (LLMs) have shown strong potential for planning and sequential decision-making, but prior work often relies on using them as direct controllers, which requires precise action generation and can be unreliable in practice. This paper proposes Latent Action Guidance for Online Reinforcement Learning (LaGO), a framework that uses a pretrained LLM as a latent action prior to softly guide online policy optimization, rather than treating the LLM as an explicit planner or controller. Experiments on both a discrete-control benchmark, CLEVR-Robot, and a continuous-control benchmark, Meta-World, demonstrate that LaGO consistently improves both reward and success rate over Vanilla PPO. In particular, LaGO increases the average success rate from 15.1% to 27.2% on CLEVR-Robot and from 2.7% to 15.2% on Meta-World. Our analysis further shows that stronger pretrained LLMs provide more effective guidance, suggesting that LLM knowledge can improve planning and online decision-making.

On-policy distillation (OPD) trains a student policy using teacher signals computed on trajectories sampled by the student itself. Recent work shows that sampled-token OPD can be fragile on long-horizon reasoning tasks and that local teacher-support matching is a simple and effective repair. This paper introduces blockwise policy-drift gating, a lightweight student-only old-current drift controller for OPD under rollout reuse. The method computes log-probability shifts between the behavior student and the current student on the sampled token path, aggregates these shifts over fixed blocks or spans, and uses the resulting detached, mean-normalized gates to reweight OPD position losses. It does not change teacher targets, teacher top-K supports, or the rollout policy. In a six-variant Qwen3 math reasoning benchmark with a uniform 200-step training budget for all trained variants, we use pass@8 as the primary problem-level solve-rate metric. Fixed 64-token block gating improves sampled-token OPD mean pass@8 from 0.4978 to 0.5160 across AIME24, AIME25, MATH500, and AMC23. On Teacher-TopK/LSM, Block64 gives the best four-benchmark mean pass@8 among trained students. The results identify local old-current policy drift as a practical control signal for reused OPD rollouts and motivate block-level gating as a simple default for improving solve-rate robustness.

Recent work has established that regularized policy gradient methods such as PPO, when used in self-play, can match or exceed specialized game-theoretic algorithms for solving two-player zero-sum imperfect-information games. The uniform distribution has emerged as a strong policy regularization target for this purpose, but it regularizes equally toward all actions regardless of their viability. We introduce EMAgnet, which instead regularizes toward an exponential moving average (EMA) of the last-iterate policy's parameters, providing an adaptive regularization target that evolves with the agent's improving strategy. We evaluate EMAgnet on both standard two-player zero-sum benchmarks and modified benchmarks with exploration challenges and large numbers of strictly dominated strategies. Relative to PPO self-play with uniform-magnet regularization under both linear and power-law annealing schedules, EMAgnet achieves lower exploitability in the majority of tested environments, with consistent performance gains across games containing strictly dominated strategies.

Proximal Policy Optimization (PPO) is the standard policy-gradient algorithm for on-policy reinforcement learning. The literature presents it in two forms, a clipped surrogate that bounds the importance ratio between successive policies and a Kullback-Leibler penalty between them. These forms are treated as separate algorithms with their own gradients, their own hyperparameters, and their own reference implementations, and a sizeable body of empirical work compares them. We show that the gradient of the clipped surrogate is reproduced exactly by a Kullback-Leibler surrogate whose coefficient varies per sample, with closed-form dependence on the importance ratio and the advantage. The identity holds at every minibatch step and across the entire inner loop, and on five MuJoCo continuous-control benchmarks the two losses produce indistinguishable training curves. The reformulation exposes a structural feature of the clipped surrogate that the min notation hides. PPO-Clip's implicit per-sample penalty is a step function at the boundary of the trust region, and the shape of this coefficient is the natural design axis for generalising the algorithm. We sketch the resulting follow-up directions in the discussion.

In many modern applications of reinforcement learning (RL), the natural reward for a task of interest is inherently sparse: a reward of 0 is given everywhere except when the task is completed, when a reward of +1 is given. Training a policy to maximize such a sparse reward requires solving a challenging credit assignment problem, leading to slow or ineffective RL improvement. We propose a simple approach to transform a sparse outcome reward into a dense process reward. Our approach relies on training a discriminator to distinguish between previous successful and unsuccessful episodes, and using this discriminator to incentivize the RL-learned policy to match the state-action visitations of successful episodes, while avoiding those of unsuccessful episodes. By incentivizing the policy to match the visitations over all states, not just those that correspond to task success, this reward provides dense feedback on whether progress is being made towards task completion, and, we show, provably achieves this without changing the optimal policy. Focusing on finetuning of robotic control policies, we demonstrate that our approach leads to significantly faster RL finetuning performance on both simulated and real-world manipulation tasks, as compared to simply maximizing the sparse outcome reward.

On-Policy Distillation (OPD) improves the learning efficiency of standard reinforcement learning through dense, token-level supervision from teachers. In the standard KL objective of OPD, token-level losses are uniformly averaged, implying equal weights for all tokens. However, we discover that not all tokens are created equal: as student rollouts grow longer, they deviate further from the teacher's distribution, leading to degraded supervision quality at later positions. As a result, OPD using only the first 30% of tokens can perform comparably to using all tokens, whereas OPD using only the last 30% of tokens barely learns anything. In this work, we provide a principled understanding of this issue through the lens of constrained optimization. Based on these insights, we derive Importance-Weighted On-Policy Distillation (IW-OPD), in which the weight assigned to each token depends on the accumulated discrepancy between the student's and teacher's distributions, naturally upweighting earlier tokens and downweighting later ones with larger deviations. We show that IW-OPD converges significantly faster than OPD, with better learning efficiency, and achieves better final performance than standard OPD in both same-size and cross-scale settings, improving performance up to 6.9 points on AIME-2025.

Multi-turn agents interleave consequential decisions with routine execution: some actions change the downstream return distribution, while others are necessary but reward-equivalent. The cost of trajectory-level credit assignment, often attributed to long horizons, is in fact governed by decision density $ρ$: the fraction of turns whose actions affect the return. When decision density is low, routine turns create signal dilution: they add gradient variance to trajectory-level estimators such as GRPO without adding expected signal. Under explicit assumptions, the resulting turn-level to trajectory-level signal-to-noise ratio scales as $ρ^{-1/2}$, provided critic error remains controlled. The same analysis identifies the complementary regime: at high decision density, trajectory-level methods can remain competitive while avoiding the cost of a critic. In a controlled environment where $ρ$ is exactly tunable, the predicted scaling is recovered with $R^2 = 0.999$, and the training-step gap widens significantly as $ρ\to 0$.

Reinforcement learning (RL) has become central to LLM post-training, yet the methods that dominate current pipelines, PPO and GRPO, represent only a narrow slice of what RL offers. Understanding why these methods prevail, and what alternatives exist, requires a principled examination of the design decisions that underlie any RL algorithm. This survey organizes that examination around three stages of algorithm construction. We begin with MDP creation: how the reward function, state space, action space, termination condition, and discount factor are, or could be, defined for LLM training. We then turn to exploration, covering temperature sampling, entropy regularization, intrinsic motivation, tree search, and curriculum learning. Finally, we address learning along four classical RL dimensions: model-free versus model-based, value-based versus policy-based versus actor-critic, on-policy versus off-policy, and credit assignment, including both Monte Carlo methods, which rely on full return estimates, and bootstrapping methods, which update estimates using other learned predictions. Mapping the LLM literature onto this taxonomy reveals a strikingly non-uniform distribution of research effort. Critic-free policy gradients and Monte Carlo credit assignment are densely populated, while value-based methods, off-policy actor-critic training, and bootstrapping-based credit assignment remain largely unexplored despite well-established counterparts in classical RL. These gaps represent concrete opportunities for transferring proven RL techniques to LLM training. By making these gaps explicit alongside the methods that have proven effective, this survey offers researchers in both RL and LLMs a shared framework for understanding current practice and identifying promising directions for future work.

Model-free reinforcement learning algorithms such as Proximal Policy Optimization (PPO) treat the environment as a black box, estimating policy gradients from sampled rewards; this process demands millions of interactions and relies on high-variance advantage estimates. When environment dynamics are differentiable, the return is an end-to-end differentiable function of the policy parameters, enabling exact gradient computation via backpropagation through simulation. We term this approach Analytic Policy Gradients (APG) and evaluate it against PPO on four continuous control tasks of increasing dynamical complexity: a one-dimensional point-mass target-reaching task, a 2D point-mass navigation task with obstacle avoidance, a 2D rigid-body T-block pushing task, and a 7-DOF Franka FR3 end-effector reaching task. Both algorithms share identical model architectures, observation normalization, and optimizer settings. To decouple sample efficiency from compute efficiency, we design a multi-axis evaluation protocol that records performance against environment steps and gradient steps. We report a segmented backpropagation scheme with MC and critic-based bootstrap modes that mitigates gradient degradation on long-horizon tasks, and present ablations over segment length and bootstrap strategy.

Self-improvement can self-regress. In REINFORCE post-training for code, a model can quickly improve on its optimized metric and then collapse within the same training campaign. We study this in a controlled multi-seed testbed using Qwen-2.5-3B and Qwen-2.5-7B, trained on competitive-programming tasks with binary CodeGrader reward across 10 sequential 20-step campaigns. Across campaigns, pass@1 shows a robust rise-then-collapse pattern: it peaks within tens of gradient steps and then falls back, sometimes to near zero. This is not cross-task catastrophic forgetting, but within-task policy over-optimization on a fixed distribution; KL- and EWC-style constraints do not prevent it. We ask where the control loop should sit. We compare three levels: CARE, a between-campaign memory mechanism with a capability posterior, transfer gate, and regression-aware belief revision; ES, a within-campaign early-stop rule that rolls forward the peak checkpoint and sets the next budget to peak_step+3; and GRPO, which changes the RL update using group-relative reward normalization. The answer is regime-dependent. On Qwen-2.5-3B, where naive REINFORCE is fragile, CARE v2 nearly doubles end-of-chain pass@1 from 4.9% to 9.5%, with paired bootstrap 95% CI [+0.4,+8.9] and gains in 4/5 seeds. On Qwen-2.5-7B, CARE reaches parity with naive REINFORCE, 13.8% vs. 11.8%, while ES reaches 22.2% [14.1,28.0]. Out-of-the-box GRPO reaches 20.7% [15.7,25.1], nearly matching REINFORCE+ES. GRPO raises the floor but does not remove the cliff. Its 7B gain mainly comes from better between-campaign carryover, while the within-campaign peak-to-end gap remains about 17 points under both REINFORCE and GRPO. GRPO+ES gives mixed evidence: 2/3 seeds improve, but one final cliff lowers the mean to 17.0% [0.0,28.1]. A Gemma-3-4B pilot shows the same signature, suggesting the phenomenon is not limited to Qwen.

We present Pareto Q-Learning with Reward Machines (PQLRM), a multi-objective reinforcement learning algorithm for tasks whose reward structure is specified by a set of reward machines (RMs). PQLRM combines Pareto Q-Learning (PQL), which maintains sets of vector-valued Q-estimates to approximate the Pareto front, with enhancements from Q-Learning with Reward Machines (QRM), which exploits the factored automaton structure of the reward signal. This yields a multi-policy algorithm that remains sample-efficient under non-Markovian, RM-encoded rewards. Experimental trials show that PQLRM converges faster than a naive PQL baseline applied to the cross-product MDP and can synthesize Pareto-optimal policies that QRM cannot.

Reinforcement learning pipelines for Large Language Model (LLM) training often rely on manually redesigned environments between stages, requiring practitioners to heuristically infer which configuration will best improve the current policy. To automate this process, we propose the LLM-as-Environment-Engineer framework in which the current policy model analyzes failure trajectories together with contextual information and proposes modifications to the next-stage training environment configuration. We also introduce MAPF-FrozenLake, a controllable testbed whose generator exposes multi-dimensional environment configurations, making it suitable for studying and benchmarking environment redesign. On this testbed, we condition the environment engineer on structured summaries of policy behavior, failure cases, and environment statistics, from which it produces the configuration for the next training stage. With Qwen3-4B as the backbone, our framework achieves the strongest aggregate performance on our benchmarks, outperforming larger proprietary LLMs (e.g., GPT, Gemini) and fixed-environment training baselines. We further analyze which forms of context are most effective, finding that successful environment updates rely on failure evidence and preserve configurations that already work. Interestingly, the current RL checkpoint serves as a better environment engineer than the original base model, suggesting that policy learning improves the model's ability to diagnose its remaining weaknesses.

Reinforcement learning (RL) has emerged as a powerful paradigm for training Large Language Models (LLMs) as agents. However, conventional RL methods for long-horizon agentic tasks often struggle with sparse outcome rewards. Intuitively, this overlooks the rich environment dynamics information contained in rollout interaction trajectories. We argue that the interaction experience inherently serves as an implicit supervision signal, reveals the underlying transition mechanisms of the environment, and enables the agent to construct a more accurate internal model of the environment.. Therefore, in this work, we investigate how to leverage this additional signal to improve policy learning. Specifically, we propose EnvRL, a framework that incorporates environment dynamics learning into agentic RL via two auxiliary objectives: state prediction and inverse dynamics. By jointly optimizing with the primary RL objective, we encourage the agent to internalize environment dynamics from its own interaction experience. Extensive experiments on two long-horizon agentic benchmarks demonstrate that EnvRL achieves significant improvements on success-rates over RL-only baselines, e.g., when trained with GRPO, lifting Qwen-2.5-1.5B-Instruct from 72.8% to 77.4% on ALFWorld, and from 56.8% to 67.0% on WebShop.