Sample-Efficient RL

Augmenting model-free reinforcement learning (RL) with representations learned through observation dynamics prediction (observation-predictive RL) can improve sample efficiency and performance, with minor modifications and limited additional computation. However, this approach still struggles in challenging tasks with low-dimensional observations. In this paper, we identify a key factor behind this problem: unbalanced reconstruction losses across observation dimensions, where dimensions with larger value ranges dominate the loss. This encourages the agent to neglect dimensions with relatively small ranges, leading to degraded performance. To address this issue, we propose a novel normalization method tailored to online RL, which normalizes low-dimensional observations and balances the resulting losses and gradients. Beyond balancing reconstruction losses, observation normalization enables dynamics prediction to be performed in a normalized observation space, thereby providing a unified treatment of low- and high-dimensional inputs (e.g., physical states and images). Building on this idea, we further introduce Normalized Observation Space Dynamics-Augmented Q-learning (NASDAQ), a framework for observation-predictive RL applicable across diverse domains. NASDAQ learns state-action representations by coupling value learning with two auxiliary tasks: short-term value prediction and next normalized observation prediction. Extensive experiments demonstrate that NASDAQ achieves competitive or superior performance compared with state-of-the-art model-based and self-predictive RL methods, while requiring significantly less training wall-time.

Direct Advantage Estimation (DAE) has been shown to improve the sample efficiency of deep reinforcement learning algorithms. However, its reliance on full environment observability limits its applicability in realistic settings, and its requirement to model transition probabilities incurs substantial computational overhead for high-dimensional observations. In the present work, we address both limitations. First, we extend the theoretical framework of DAE to partially observable domains with minimal modifications. Second, we reduce its computational complexity by introducing discrete latent dynamics models that efficiently approximate transition probabilities. We evaluate our approach on the Arcade Learning Environment and find that DAE scales effectively with function approximator capacity while retaining high sample efficiency.

A natural recipe for intelligent robotic decision-making is initializing from pretrained generative control policies, which have summarized offline experience, and adapting them to self-collected online experience. We present DF-ExpEnse, an exploration technique that improves the quality of online experience collection, thus increasing finetuning sample-efficiency. DF-ExpEnse leverages the multimodal modeling capabilities of the generative control policy to create an expressive and tractably evaluatable candidate set. It then utilizes an ensemble of critics to identify the action that best balances quality with high exploration interest. In fleet settings, DF-ExpEnse further enables cross-agent communication to facilitate collaborative exploration as a group. DF-ExpEnse can be seamlessly integrated with existing strategies that finetune pretrained generative control policies via reinforcement learning. We experimentally validate consistent sample-efficiency benefits through DF-ExpEnse across a variety of manipulation and locomotion tasks, compared to default finetuning and alternative action selection schemes. Project can be found at https://df-expense.github.io.

Preference-based RL provides an approach to learning reward models from pairwise comparisons of behaviors, bypassing the need for explicit reward design. However, existing methods typically rely on passive data collection and suffer from poor sample efficiency, especially during the early stages of learning. We introduce a model-based approach that actively directs exploration by jointly reasoning over uncertainties in the reward, dynamics, and value functions. Our method, Uncertainty-Balanced Preference Planning (UBP2), uses ensembles of reward, dynamics, and value function models to evaluate candidate trajectories according to a unified score that combines expected reward, terminal value, and epistemic uncertainty. Planning under this objective yields an explicit tradeoff between exploitation and information acquisition without requiring ad hoc exploration heuristics. Under standard regularity assumptions, we establish sublinear regret guarantees for both finite-horizon and infinite-horizon settings. Empirically, experiments on the Meta-World benchmark show UBP2 achieves substantially higher sample efficiency than model-free preference-based methods and non-optimistic model-based baselines.

Multi-turn tool-use RL is bottlenecked by the rapid depletion of informative samples in static datasets. We observe that the gradient signal in GRPO concentrates on tasks with the highest rollout reward variance, a consequence of the Popoviciu upper bound. Consequently, samples near the agent's capability boundary -- where successes and failures are roughly balanced -- contribute disproportionately large policy gradients. As training progresses, this boundary continuously shifts, which gradually depletes the pool of informative samples in a static dataset. We propose RODS (Reward-driven Online Data Synthesis) to resolve this depletion. RODS closes the loop between RL training and data generation by repurposing the progress reward variance as a practical, zero-cost boundary detector that requires no extra inference beyond the rollouts already computed for training. It continuously identifies such boundary samples, synthesizes new multi-turn variants matching their structural complexity (e.g., API topology and dependency depth) via a skill-aligned resampling pipeline, and manages a dynamic replay buffer that co-evolves with the policy. Starting from 400 human seeds and maintaining an active training pool of ~800 samples, RODS achieves comparable performance to a 17K-sample offline pipeline while requiring roughly 20x fewer trajectories, and improves over fixed-data RL and environment augmentation in our controlled setting.

We study performance-driven environment abstraction for decision-making in large Markov decision processes. Rather than preserving geometric or topological structure, we seek abstractions that directly optimize decision quality. We model abstraction as a controlled approximation obtained by aggregating the state space and enforcing a shared action distribution within each aggregated state. For a fixed partition, we establish a performance guarantee that separates value-function approximation error from the loss introduced by action sharing. Guided by this analysis, we develop a multi-timescale reinforcement learning framework that jointly adapts the policy and a tree-structured environment abstraction. The resulting algorithm refines and coarsens regions of the state space based on Q-value discrepancies, balancing performance against abstraction size and complexity. Empirical results demonstrate substantial state compression, improved sample efficiency, and faster replanning compared to actor-critic baselines.

While there is an extensive body of work characterizing the sample complexity of discounted cumulative-reward MDPs, finite sample analyses for average-reward MDPs have been limited, and most existing works rely on restrictive assumptions such as ergodicity or access to a generative model. In this work, we establish the first finite sample complexity guarantees from a single trajectory for weakly communicating average-reward MDPs. To this end, we study the dynamics of a single trajectory in weakly communicating MDPs and based on this analysis, we develop novel model-free methods. Notably, our value-based and policy-based methods provide finite sample complexity guarantees of $\widetilde{O}(1/\varepsilon^2)$ and $\widetilde{O}(1/\varepsilon^4)$ from a single trajectory in weakly communicating MDPs, respectively. Furthermore, we introduce the first model-free method that requires no prior knowledge of problem-dependent quantities for communicating MDPs.

Exploration in deep reinforcement learning (RL) is commonly implemented as temporally uncorrelated white noise. However, recent works show that temporally correlated colored noise can improve exploration efficiency by producing smooth trajectories with better coverage of the state space. We inquire whether action noise inspired by infant spontaneous movements can also improve exploration in deep RL. We find that the power spectral densities of babies' end-effector velocities follow a colored noise process where the spectral exponent increases with age. Inspired by this developmental pattern, we introduce a mechanism that progressively increases the temporal auto-correlation of exploration noise during RL training, matching the infant statistics. Experiments across several RL environments show that infant-inspired noise produces structured exploratory behavior and can improve learning efficiency compared to conventional exploration strategies. These findings suggest that human motor and cognitive development can provide useful guidance for designing learning mechanisms in artificial agents. Our code is available at https://github.com/trieschlab/baby-noise-rl.

We study the sample complexity of learning in average-reward weakly-coupled Markov decision processes (WCMDPs) and Restless Bandits (RBs) under a generative model. Naive reduction to a tabular MDP leads to high complexity bounds as the state-action space is exponentially large in the number of arms $N$. By exploiting the weakly coupled structure, we show that near-optimal policies can be learned with sample and computational complexities that are polynomial in $N$. Specifically, we analyze the plug-in approach, which applies an efficient planning algorithm to an empirical model estimated from data. For fully heterogeneous WCMDPs, we establish the first finite-sample PAC guarantee with polynomial complexity and an $O(1/\sqrt{N})$ optimality gap. For homogeneous RBs, we further prove that a smaller optimality gap is achievable under mild structural assumptions. A primary technical contribution of our work is a novel Lyapunov-based analysis framework. Unlike classical approaches that rely on the difficult-to-control bias function, our framework uses an explicitly constructed Lyapunov function along with a drift transfer technique between the true and empirical models. A key step of independent interest in our framework is a fine-grained perturbation analysis for the underlying linear programming (LP) relaxation, which provides a general tool for analyzing LP-based policies and weakly-coupled systems.

Reinforcement learning with verifiable rewards (RLVR) is a promising approach for enhancing reasoning and agentic behavior in large language models. However, rollout-intensive policy optimization is often limited by insufficient reward contrast, arising when overly simple or complex prompts generate low-variance feedback and when outcome-only rewards assign the same terminal assessment to every decision in a multi-turn rollout. Past efforts have focused on allocating available rollout resources to promising prompts, yet they only leverage sample informativeness at the prompt level and neglect variation in prefix-level informativeness across turns within the same rollout. This work targets multi-turn agentic RL by modeling each ReAct-style thought-action-observation turn as a semantically distinct node, allowing budget allocation to extend from prompt roots to turn-level prefixes with further continuations, which naturally forms tree-structured rollouts. We introduce Tree Rollout Allocation for Contrastive Exploration (TRACE), a unified rollout allocation framework that enhances reward contrast within a fixed sampling budget. Technically, TRACE allocates rollout budget to both prompt roots and intermediate prefixes that are most likely to yield mixed terminal rewards. A shared generalizable predictor estimates conditional success probability at these anchors from prefix histories to guide this allocation. The resulting adaptive tree structure enriches outcome-only feedback and amplifies the policy-update signal. Empirically, TRACE achieves competitive performance and efficiency gains on typical agentic benchmarks, e.g., improving Qwen3-14B Multi-Hop QA average accuracy by 2.8 points over competitive baselines at equal sampling cost.

Current reinforcement learning from human feedback (RLHF) methods primarily rely on scalar rewards from a trained reward model (RM). While effective, scalar rewards are often noisy and fail to capture fine-grained preference differences, whereas RM hidden states encode richer semantic and preference information. We introduce the representation-aware advantage estimation, which leverages RM hidden states and models them as auxiliary signals for better advantage estimation. Specifically, we propose the Graph-based Advantage Estimation (GraphAE), treat each sampled group as a graph, where nodes correspond to responses and edges capture their similarity in the RM hidden space. Then advantages are computed via graph propagation, enabling each sample to incorporate contextual information from its neighbors. GraphAE is lightweight and can be seamlessly integrated into existing group-based RL algorithms. We apply GraphAE to GRPO, GSPO and RLOO, and conduct extensive experiments on different models and benchmarks. Empirical results show consistent improvements across three benchmarks, with gains of up to + 6.3 on Arena-Hard-v0.1, + 8.27 on AlpacaEval 2.0, and + 0.22 on MT-Bench. These results demonstrate that leveraging RM representations leads to more sample efficient and robust RLHF.

Training large language models (LLMs) as autonomous agents via reinforcement learning (RL) has enabled frontier models to achieve superhuman performance in long-horizon tasks. However, existing RL algorithms operate at the trajectory level, performing policy optimization only after collecting complete episode rollouts. This coarse-grained approach faces fundamental challenges in multi-turn agent settings where rewards are sparse, delayed, and credit assignment across individual steps is critical. In this work, we propose \textbf{State-Score-Supervised Policy Optimization (3SPO)}, a novel RL algorithm that performs post-step policy optimization with dynamic state score supervision. At each step, 3SPO computes the state score based on historical success rates, supervising step-wise credit assignment, adaptive rollout and post-step policy optimization without requiring value function estimation or additional auxiliary models. Theoretically, under a per-state bandit abstraction, we show that the proposed score-supervised allocation mechanism achieves logarithmic allocation regret and provide sample-complexity guarantees for action identification, score distinguishability, and filtering stability. Experiments on ALFWorld and WebShop with Qwen2.5-1.5B/7B-Instruct show that 3SPO consistently outperforms GRPO by $+22.6\%$ on ALFWorld and $+15.6$ points on WebShop, while using comparable resources to achieve $2.4\times$ more state exploration and $1.8\times$ faster convergence. Code is available at https://github.com/genalyu/3SPO.

Standard Reinforcement Learning with Verifiable Rewards (RLVR) training allocates a fixed rollout budget to every query, without regard for what each query's difficulty means for the current policy. This leads to two symmetric failure modes: easy queries produce near-zero advantage because the policy already solves them, while unsolvable queries produce no signal because the policy never solves them. Both regimes waste training FLOPs without contributing to a learning gradient. We introduce sorted Group Policy Optimization (sGPO), a compute-efficient strategy that trades a small budget of inference FLOPs for a large reduction in wasted training FLOPs. The key insight is that cheap inference compute can serve as a single offline proxy for query difficulty. By generating a small batch of parallel samples per query under the initial policy, we obtain a model-aware empirical success rate. This motivates setting the training rollout group size to the inverse of this success rate, a practical rule that maximizes sample efficiency by extracting the most advantage per generated rollout. This single profiling pass simultaneously drives data filtering (removing trivial queries and sub-sampling unsolvable ones), adaptive group size allocation, and curriculum construction (scheduling queries from easy to hard). sGPO matches or exceeds baseline performance while reducing total training compute by a factor of three, with the upfront inference profiling cost included.

LLM post-training often relies on reinforcement learning methods that sample multiple rollouts per prompt, yet most existing approaches use a fixed rollout budget for every prompt, despite large differences in the training signal different prompts provide. In this paper, we study adaptive rollout allocation under a fixed global budget and formulate the problem as online resource allocation with prompt-level diminishing returns. Our method, CERO, maintains a Beta posterior over each prompt's success probability and uses the posterior expected Bernoulli variance as a Bayesian estimate of the value of additional rollouts. We use this estimate to construct a concave, saturating utility over cumulative allocations, yielding an objective in which decisions across prompts and epochs are coupled by the global budget. Since the resulting objective is temporally nonseparable, we derive a Fenchel-dual reformulation and update both prompt-level and budget-level dual variables via projected online gradient descent. Under fixed prompt utilities, we prove an $O(\sqrt{K})$ regret bound against the offline allocation benchmark. Experiments on mathematical-reasoning problems show that CERO consistently outperforms GRPO across multiple open-weight LLMs and benchmarks, demonstrating that adaptive rollout budgeting can improve sample efficiency.

Reinforcement learning from verifiable rewards with GRPO is a standard approach for post-training reasoning LLMs. It remains sample inefficient. Each rollout is used for a single gradient update and then discarded. Naive replay is not well suited in this setting because LLM policies drift quickly per gradient step. Stored rollouts therefore become stale and can destabilize training. We propose a rollout-level replay buffer for GRPO that stores and samples individual rollouts rather than whole groups. The buffer bounds staleness through age eviction. Any rollout older than tau_max training steps is removed. The buffer also preserves on-policy data via fresh-anchored composition. Each batch keeps its fresh on-policy rollouts and then concatenates replay rollouts drawn separately from the buffer. We prioritize replay by per-rollout advantage magnitude and recycle individual rollouts whose advantages are large. Across three Qwen3-Base scales on five math benchmarks, our method outperforms GRPO and naive replay baselines. Gains are positive at every scale and reach +1.66 pp on the five-benchmark average at 4B. Under an AES metric that jointly measures accuracy and token efficiency, our method is the only condition with a positive margin over GRPO at every scale.

Reinforcement learning with verifiable rewards (RLVR) has emerged as a powerful paradigm for enhancing the reasoning capabilities of large language models (LLMs). However, its effectiveness is substantially hindered by the prevalence of ineffective training data: many sampled prompts yield response groups that are either entirely correct or entirely incorrect, resulting in zero-variance rewards and limited learning signals. Recent state-of-the-art methods address this issue through extensive LLM rollouts to filter ineffective samples, but at the cost of considerable computational overhead. Alternative approaches, including predictive sampling and trajectory replay, aim to improve data efficiency but often remain insufficient and may introduce additional issues such as systematic bias or suboptimal constraints. To address these limitations, we propose Group Prioritized Off-Policy Optimization (POPO), a simple yet effective framework that fully exploits effective training batches without additional rollout overhead. POPO comprises two key components: prioritized group replay and decoupled off-policy optimization. The former replaces ineffective on-policy groups with effective off-policy groups via a recency-based replay mechanism that jointly considers sample quality and the degree of off-policiness. To further mitigate the off-policy gap, POPO employs decoupled importance sampling to correct off-policy bias while maintaining stable policy updates under consistent trust-region constraints. Empirical evaluations across diverse reasoning tasks, including mathematics, planning, and visual geometry, demonstrate that POPO substantially accelerates RL finetuning and achieves strong reasoning performance with significantly fewer rollouts.

Behavior cloning with high-capacity generative policies achieves strong imitation performance, but is often limited by demonstration coverage and distribution shift. Direct reinforcement learning fine-tuning can improve performance, but updating large action decoders is frequently unstable and sample inefficient. We propose Lagrangian Perturbation Diffusion Steering (LP-DS), a lightweight adaptation method that improves a frozen generative policy by learning a compact noise-space perturbation before decoding. LP-DS optimizes this perturbation with a Lagrangian trust-region objective, improving downstream value while constraining deviation from the latent prior. Across RoboMimic manipulation, OpenAI Gym locomotion, and Adroit dexterous manipulation benchmarks, LP-DS improves sample efficiency, success, and return while maintaining higher action-space entropy than unconstrained noise-space steering, with return improvements of up to 25% over prior baselines. Additional evaluations with flow-matching backbones, a large vision-language-action model, and physical Franka deployment show that LP-DS is not limited to compact diffusion policies or simulated benchmarks. Project page: https://sites.google.com/view/lp-ds/home.

Reinforcement learning problems typically define the goal as maximizing the expected value of a scalar reward function. But, pairwise preferences are often easier to specify than scalar rewards, and they express certain goals that scalar rewards cannot. Methods for reinforcement learning with pairwise preferences have thus received growing interest. Unfortunately, these methods are inefficient in problems with long time horizons, and they lack guarantees on the performance of Markov policies relative to history-dependent policies, which bridge the theory and practice of reinforcement learning. We therefore propose the \textit{Markov decision contest} as a new problem model for reinforcement learning with pairwise preferences. We prove that stationary Markov policies are optimal among all history-dependent policies, that solving a Markov decision contest exactly is in P, and that a simple iterative algorithm converges to an optimal policy at a sublinear rate. Lastly, in a set of high-dimensional decision problems with long time horizons, we show that our approximate algorithm is significantly more learning-efficient than prior work.

LLM-based LEGO assembly generation requires both semantic grounding and physical feasibility. We identify a data-induced failure mode, PhysHack, in which the assemblies satisfy physical-validity constraints while producing structures that are geometrically misaligned, semantically inconsistent, or poorly calibrated. To address this challenge, we propose a model-based data selection approach that uses only a small fraction of the training data while improving physically grounded LEGO assembly generation. Building on the selected trajectories, we introduce PVPO, a sample-efficient reinforcement learning method that couples physical feasibility with voxel-space geometric rewards. Our results show that physical validity alone is an insufficient proxy for reliable physical reasoning: models can learn to generate valid structures without preserving semantic or geometric fidelity. Experiments across model backbones and test-time scaling settings demonstrate that PVPO improves structural and semantic alignment, physical validity, structural stability, and calibration, while reducing reliance on extensive post-hoc rejection sampling. In particular, results on calibration show that PVPO mitigates PhysHack by making test-time selection more predictive of semantic and structural quality.

Recent advances in reinforcement learning (RL) have achieved great successes by leveraging the multimodality and exploration capability of diffusion policies. Among these approaches, one representative branch focuses on the sampling-based policy optimization. This design enables better exploration capability of the diffusion model, particularly at the beginning of training, but suffer from low exploitation in Q-value information, resulting in a slow policy convergence. Another branch pays attention to gradient-based policy optimization, which sufficiently exploits the gradient of the Q function yet tends to collapse into a unimodal policy with low diversity. To address this issue, we propose CGPO, \textbf{C}ritic-\textbf{G}uided diffusion \textbf{P}olicy \textbf{O}ptimization, which effectively balances exploration and exploitation with the training-free guidance technique integrated into the denoising process of diffusion policy. Concretely, CGPO steers action generation toward high-value regions defined by the critic network and uses the guided actions as regression objectives. In this manner, CGPO reduces the time required to obtain high-quality actions and improves final performance with better balance between the exploration-exploitation tradeoff. We validate the effectiveness of CGPO on 5 MuJoCo locomotion tasks, and CGPO achieves state-of-the-art performance compared with existing diffusion-based RL methods. Notably, CGPO is the first success to incorporate diffusion policy into real-world RL, with its superior performance on Franka robot arm grasping tasks. Our official page is released at https://dingsht.tech/cgpo-webpage.

Data acquisition efficiency is a central challenge in deploying reinforcement learning in business and healthcare operations, where interactions are costly, slow, and often involve humans in the loop. This paper develops a unified large deviations framework for data acquisition in infinite-horizon reinforcement learning. We introduce the exponential decay rate of the policy-selection error probability as a principled efficiency metric and derive a variational characterization of this rate via large deviations theory for Markov chains, yielding a nested optimization problem. Based on this characterization, we formalize two complementary notions of optimality in terms of the optimal solution of the nested problem. Because the resulting program is implicit and generally intractable, we propose a tractable convex relaxation with explicit constraints. We then develop a lazy one-step projected subgradient method to solve the relaxed problem and use its iterates to construct an adaptive data acquisition policy. We prove that the resulting reinforcement learning algorithm is near-robustly optimal under our optimality criterion, up to a constant factor. Finally, we extend the framework to linear function approximation to improve scalability, and numerical experiments support the effectiveness of the proposed approach.

Reinforcement learning with verifiable rewards (RLVR) has become a key technique for en- hancing LLM reasoning, yet its data ineffi- ciency remains a major bottleneck. Existing methods address this problem only partially, each missing at least one of subset-level cov- erage, verifier signal use, or interpretability. To address this gap, we present IRDS (Inter- pretable RLVR Data Selection), which selects RLVR training instances on a sparse autoen- coder (SAE) cluster basis so the selection itself is auditable on recognizable problem motifs. To select instances the model both fails on and can still learn from, we introduce a verifier- coupled coverage objective on the SAE basis and solve it by greedy log-determinant max- imization. Experiments on three instruction- tuned models and six math reasoning bench- marks show that IRDS achieves the highest overall accuracy, exceeding the strongest base- line by +3.9/+4.0 pp on the two Qwen models and by +0.5 pp on Llama-3.1-8B, while run- ning an order of magnitude cheaper than the trajectory-based baseline.

Reinforcement learning with verifiable rewards has become a standard recipe for improving the reasoning abilities of large language models. Existing algorithms face a tradeoff between computational efficiency and sample efficiency in value estimation and policy learning. We introduce BASIS, a critic-free post-training algorithm designed to address this tradeoff. At each online training step, BASIS samples only one rollout per prompt, but leverages rich information across prompts in the entire batch to improve value function estimation. Our experiments demonstrate that BASIS reduces MSE in value function estimation by 69% compared to REINFORCE++, a representative single-rollout baseline, and achieves lower MSE with one rollout than group mean estimators with 8 rollouts. This improvement in value estimation translates to better policy optimization: using substantially less training time, BASIS achieves performance close to multi-rollout GRPO-type baselines and often outperforms single-rollout REINFORCE-type baselines.

Standard on-policy reinforcement learning relies on heuristic clipping to enforce trust regions, but this mechanism imposes a severe cost by indiscriminately truncating high-return yet high-divergence updates. We demonstrate that explicitly constraining the policy ratio variance provides a principled local approximation to trust-region constraints, eliminating the need for binary hard clipping. By acting as a distributional ``soft brake'', this approach preserves critical gradient signals from novel discoveries while naturally down-weighting and enabling the reuse of stale, off-policy data. We introduce ${\bf R}^2{\bf VPO}$ (Ratio-Variance Regularized Policy Optimization), which implements this constraint via a primal-dual optimization framework. Extensive evaluations across $7$ LLM scales, spanning both fast and slow reasoning paradigms, and $10$ robotic control tasks demonstrate the generality of the proposed approach. R$^2$VPO achieves substantial performance gains on mathematical reasoning benchmarks, with particularly pronounced improvements on smaller models, while significantly improving sample efficiency. Furthermore, it consistently outperforms PPO baselines in continuous control domains, particularly in sparse-reward and dynamic environments. Together, these findings establish ratio-variance regularization as a principled foundation for stable and data-efficient policy optimization.

We study the sample complexity of policy gradient for log-growth control -- the problem of learning, from observed state transitions, a feedback gain that optimally stabilizes a scalar linear system driven through a multiplicative-noise actuation channel. The objective $J(K) = \mathbb{E}[\log|1+BK|]$ is the top Lyapunov exponent of the closed loop. This problem carries a structural difficulty we call the cusp obstruction: the optimal gain $K^*$ always places the noise singularity $b_{\rm sing}(K) = -1/K$ in the interior of the support. At this singular optimum the policy gradient exists only as a Cauchy principal value, not as a Lebesgue integral, and the natural single-sample gradient estimator has infinite variance. Standard first-order stochastic-optimization analysis is thus inapplicable at the optimum, and merely smoothing the objective does not resolve the difficulty. The obstruction, however, has an exploitable symmetry: the Cauchy kernel is an odd function of the displacement from the moving pole, so pairing each observation with its reflection through the pole cancels the divergent part. This one cancellation simultaneously controls the population curvature, the gradient-estimator variance, and the bias incurred when the noise density is estimated. Combining these bounds with a closed-form single-transition gradient oracle, we prove that projected mini-batch policy gradient, initialized in any compact subset of the stabilizing region, attains total sample complexity $\tilde{O}(1/η)$ when the noise density is known and $\tilde{O}(η^{-(2s+1)/(2s)})$ when it must be estimated, for $C^s$ noise densities with $s \geq 2$.

The ability to efficiently and reliably learn new tasks has been a foundational challenge in robotics. Vision-Language-Action (VLA) models have demonstrated strong generalization across diverse manipulation tasks, yet pretrained policies consistently fall short of the reliability required for real-world deployment. Reinforcement learning (RL) fine-tuning offers a promising path to bridge this gap, but existing approaches either train from scratch without fully leveraging pretrained priors, or fine-tune VLAs without achieving the sample efficiency and success rates that practical deployment demands. We present EXPO-FT, a system for stable, sample-efficient RL finetuning of pretrained VLA policies that closes this gap. Our system solves a suite of challenging manipulation tasks, including routing string lights and inserting the plug to light it up, striking a pool ball into a pocket, and inserting a flower into a wine bottle, each requiring combinations of high precision, dynamic actions, and robustness to varied initial states. Our system achieves perfect task performance (30/30 successes) across all evaluated tasks within an average of 19.1 minutes of online robot data, outperforming both prior RL-from-scratch and VLA finetuning approaches. We release an open-source codebase with the aim of facilitating broader adoption of RL finetuning of VLA models in robotics.

Autonomous parking demands precise low-speed maneuvering within narrow, cluttered, and highly constrained environments, where vehicles must navigate tight spaces while avoiding static obstacles and complex geometric boundaries. Unlike imitation learning, which typically requires massive volumes of high-quality expert demonstrations to converge to a stable policy and often suffers from limited generalization to unseen scenarios, traditional reinforcement learning (RL) methods face persistent challenges including excessive training overhead, inefficient exploration, and even failure to learn viable parking strategies in challenging settings. To address these limitations, this paper presents a correction-in-the-loop sample-efficient reinforcement learning (CIL-SERL) framework for end-to-end autonomous parking, which is entirely trained in a photorealistic 3D Gaussian Splatting (3DGS) parking simulator that enables high-fidelity digital reconstruction of real-world scenes. Inspired by error-correction notebooks used in learning practice, we design a novel multi-level replay buffer mechanism. These buffers hierarchically organize and store standard RL rollouts, human corrective interventions, failed exploration trajectories, and rollback-based correction segments in separate yet interconnected memory regions, facilitating structured sampling and targeted learning during training. The proposed framework is systematically evaluated in both the 3DGS simulation environment and a physical vehicle platform. Extensive experimental results demonstrate that our method achieves substantial improvements in parking success rate, operational efficiency, and safety performance across diverse scenarios, validating the effectiveness and practical applicability of the proposed CIL-SERL-based end-to-end autonomous parking solution.

Proximal Policy Optimization (PPO) has become the de facto standard for training legged robots, thanks to its robustness and scalability in massively parallel simulation environments like IsaacLab. However, its on-policy nature makes it inherently sample-inefficient, preventing its use for continuous adaptation and fine-tuning on real hardware. Soft Actor-Critic (SAC), by contrast, is an off-policy algorithm that can reuse past experience, making it a natural candidate for sim-to-real transfer workflows where the same algorithm can be used both in simulation and for online learning on the real robot. Despite these advantages, SAC has consistently failed to match PPO's empirical performance in massively parallel training settings. This work identifies the root causes of this gap and introduces targeted modifications, covering policy initialization, timeout-aware critic targets, and multi-step return estimation, that enable SAC to train stably at scale. Evaluated across multiple legged robot platforms and diverse locomotion tasks, our approach closes the performance gap with PPO entirely.

In this paper, we study the role of the critic in actor--critic for entropy-regularized, finite, discounted environments. We establish that, when the critic is exact, using the latter as a baseline is a variance-reduction method in a strong sense. In this case, actor--critic with stochastic gradients matches the sample complexity of deterministic policy gradient, reaching an $ε$-optimal regularized value with $\tilde{O}(\log(1/ε))$ samples. In practice, the critic is learned alongside the actor: the variance of the actor update is then influenced by the critic's variance and bias. Specifically, when the critic has a sufficiently small error, the variance reduction and rapid convergence are preserved. This suggests to learn the critic first, keeping it up to date after each actor update, underscoring the crucial role of accurate critic estimation in actor--critic methods.

A goal-conditioned reinforcement learning agent exploring an environment will see a wealth of information throughout a trajectory, most of which is discarded when only performing on-policy updates with respect to the commanded goal. All-goals learning, where each transition is used for learning off-policy with respect to every goal, allows agents to extract maximal information, however it is usually computationally infeasible when done via naive relabelling. This can be overcome by jointly outputting values and actions for every goal at once, allowing for efficient, parallel all-goals updates with a single pass through the network, in a process we call Learning Everything all at Once (LEO). We show that this approach significantly outperforms other methods on goal-conditioned Craftax and is competitive with existing baselines on continuous control environments, while achieving a >250x speed-up compared to all-goals relabelling. We then go on to show that this approach can be made even more powerful by using LEO as a teacher network, rather than a direct actor. We hope that, by unlocking all-goals learning at scale, LEO can serve as a useful tool for RL practitioners in complex environments. We open source our code.