Online reinforcement learning (RL) typically requires online interaction data to learn a policy for a target task, but collecting such data can be high-stakes. This prompts interest in leveraging historical data to improve sample efficiency. The historical data may come from outdated or related source environments with different dynamics. It remains unclear how to effectively use such data in the target task to provably enhance learning and sample efficiency. To address this, we propose a hybrid transfer RL (HTRL) setting, where an agent learns in a target environment while accessing offline data from a source environment with shifted dynamics. We show that – without information on the dynamics shift – general shifted-dynamics data, even with subtle shifts, does not reduce sample complexity in the target environment. However, focusing on HTRL with prior information on the degree of the dynamics shift, we design HySRL, a transfer algorithm that outperforms pure online RL with problem-dependent sample complexity guarantees. Finally, our experimental results demonstrate that HySRL surpasses the state-of-the-art pure online RL baseline.

Driven by inherent uncertainty and the sim-to-real gap, robust reinforcement learning (RL) seeks to improve resilience against the complexity and variability in agent-environment sequential interactions. Despite the existence of a large number of RL benchmarks, there is a lack of standardized benchmarks for robust RL. Current robust RL policies often focus on a specific type of uncertainty and are evaluated in distinct, one-off environments. In this work, we introduce Robust-Gymnasium, a unified modular benchmark designed for robust RL that supports a wide variety of disruptions across all key RL components—agents' observed state and reward, agents' actions, and the environment. Offering over sixty diverse task environments spanning control and robotics, safe RL, and multi-agent RL, it provides an open-source and user-friendly tool for the community to assess current methods and foster the development of robust RL algorithms. In addition, we benchmark existing standard and robust RL algorithms within this framework, uncovering significant deficiencies in each and offering new insights.

A significant roadblock to the development of principled multi-agent reinforcement learning (MARL) algorithms is the fact that desired solution concepts like Nash equilibria may be intractable to compute. We show how one can overcome this obstacle by introducing concepts from behavioral economics into MARL. To do so, we imbue agents with two key features of human decision-making: risk aversion and bounded rationality. We show that introducing these two properties into games gives rise to a class of equilibria---risk-averse quantal response equilibria (RQE)---which are tractable to compute in \emph{all} $n$-player matrix and finite-horizon Markov games. In particular, we show that they emerge as the endpoint of no-regret learning in suitably adjusted versions of the games. Crucially, the class of computationally tractable RQE is independent of the underlying game structure and only depends on agents' degrees of risk-aversion and bounded rationality. To validate the expressivity of this class of solution concepts we show that it captures peoples' patterns of play in a number of 2-player matrix games previously studied in experimental economics. Furthermore, we give a first analysis of the sample complexity of computing these equilibria in finite-horizon Markov games when one has access to a generative model. We validate our findings on a simple multi-agent reinforcement learning benchmark. Our results open the doors for to the principled development of new decentralized multi-agent reinforcement learning algorithms.

Factored Markov Decision Processes (FMDPs) offer a promising framework for overcoming the curse of dimensionality in reinforcement learning (RL) by decomposing high-dimensional MDPs into smaller and independently evolving components. Despite their potential, existing studies on FMDPs face three key limitations: reliance on perfectly factorizable models, suboptimal sample complexity guarantees for model-based algorithms, and the absence of model-free algorithms. To address these challenges, we introduce approximate factorization, which extends FMDPs to handle imperfectly factored models. Moreover, we develop a model-based algorithm and a model-free algorithm (in the form of variance-reduced Q-learning), both achieving the first near-minimax sample complexity guarantees for FMDPs. A key novelty in the design of these two algorithms is the development of a graph-coloring-based optimal synchronous sampling strategy. Numerical simulations based on the wind farm storage control problem corroborate our theoretical findings.

Standard multi-agent reinforcement learning (MARL) algorithms are vulnerable to sim-to-real gaps. To address this, distributionally robust Markov games (RMGs) have been proposed to enhance robustness in MARL by optimizing the worst-case performance when game dynamics shift within a prescribed uncertainty set. RMGs remains under-explored, from reasonable problem formulation to the development of sample-efficient algorithms. Two notorious and open challenges are the formulation of the uncertainty set and whether the corresponding RMGs can overcome the curse of multiagency, where the sample complexity scales exponentially with the number of agents. In this work, we propose a natural class of RMGs inspired by behavioral economics, where each agent's uncertainty set is shaped by both the environment and the integrated behavior of other agents. We first establish the well-posedness of this class of RMGs by proving the existence of game-theoretic solutions such as robust Nash equilibria and coarse correlated equilibria (CCE). Assuming access to a generative model, we then introduce a sample-efficient algorithm for learning the CCE whose sample complexity scales polynomially with all relevant parameters. To the best of our knowledge, this is the first algorithm to break the curse of multiagency for RMGs, regardless of the uncertainty set formulation.

Deploying reinforcement learning (RL) safely in the real world is challenging, as policies trained in simulators must face the inevitable *sim-to-real gap*. Robust safe RL techniques are provably safe, however difficult to scale, while domain randomization is more practical yet prone to unsafe behaviors. We address this gap by proposing SPiDR, short for Sim-to-real via Pessimistic Domain Randomization—a scalable algorithm with provable guarantees for safe sim-to-real transfer. SPiDR uses domain randomization to incorporate the uncertainty about the sim-to-real gap into the safety constraints, making it versatile and highly compatible with existing training pipelines. Through extensive experiments on sim-to-sim benchmarks and two distinct real-world robotic platforms, we demonstrate that SPiDR effectively ensures safety despite the sim-to-real gap while maintaining strong performance.

In 5G wireless networks, the User Plane Function (UPF) plays a crucial role in efficiently transferring users’ traffic — a series of data packets — to manage internet communications. Setting the server’s processor frequency excessively high can easily meet the packet drop requirements but may lead to unnecessary power consumption. Therefore, as user traffic fluctuates, selecting the optimal processor frequency is essential for minimizing power consumption while satisfying packet drop constraints. This challenge motivates us to address the dynamic resource (frequency) allocation problem, where deep reinforcement learning (RL) has shown significant potential. Most existing studies train and evaluate the RL model in the same environment with consistent traffic patterns. However, frequent variations in user traffic can cause the policy trained on the outdated traffic to fail catastrophically on unseen traffic.To address such traffic distribution shifts, we propose a two-phase RL approach augmented with Automatic Domain Randomization (RL-ADR). This method includes a training phase that utilizes domain randomization to create a library of policy candidates, and an inference phase that selects the optimal frequency using this policy library alongside a safe data buffer. The proposed RL-ADR achieves zero packet drops on two unseen long-horizon traffics (3 hours) after being trained on 25 synthetic traffics that only span for 18 seconds. Compared to static resource allocation baselines, RL-ADR reduces power consumption by at least 14.5% and performs comparably to the oracle solution.

To overcome the sim-to-real gap in reinforcement learning (RL), learned policies must maintain robustness against environmental uncertainties. While robust RL has been widely studied in single-agent regimes, in multi-agent environments, the problem remains understudied—despite the fact that the problems posed by environmental uncertainties are often exacerbated by strategic interactions. This work focuses on learning in distributionally robust Markov games (RMGs), a robust variant of standard Markov games, wherein each agent aims to learn a policy that maximizes its own worst-case performance when the deployed environment deviates within its own prescribed uncertainty set. This results in a set of robust equilibrium strategies for all agents that align with classic notions of game-theoretic equilibria. Assuming a non-adaptive sampling mechanism from a generative model, we propose a sample-efficient model-based algorithm (DRNVI) with finite-sample complexity guarantees for learning robust variants of various notions of game-theoretic equilibria. We also establish an information-theoretic lower bound for solving RMGs, which confirms the near-optimal sample complexity of DRNVI with respect to problem-dependent factors such as the size of the state space, the target accuracy, and the horizon length.

Offline reinforcement learning (RL), which seeks to learn an optimal policy using offline data, has garnered significant interest due to its potential in critical applications where online data collection is infeasible or expensive. This work explores the benefit of federated learning for offline RL, aiming at collaboratively leveraging offline datasets at multiple agents. Focusing on finite-horizon episodic tabular Markov decision processes (MDPs), we design FedLCB-Q, a variant of the popular model-free Q-learning algorithm tailored for federated offline RL. FedLCB-Q updates local Q-functions at agents with novel learning rate schedules and aggregates them at a central server using importance averaging and a carefully designed pessimistic penalty term. Our sample complexity analysis reveals that, with appropriately chosen parameters and synchronization schedules, FedLCB-Q achieves linear speedup in terms of the number of agents without requiring high-quality datasets at individual agents, as long as the local datasets collectively cover the state-action space visited by the optimal policy, highlighting the power of collaboration in the federated setting. In fact, the sample complexity almost matches that of the single-agent counterpart, as if all the data are stored at a central location, up to polynomial factors of the horizon length. Furthermore, FedLCB-Q is communication-efficient, where the number of communication rounds is only linear with respect to the horizon length up to logarithmic factors.

To address the challenges of sim-to-real gap and sample efficiency in reinforcement learning (RL), this work studies distributionally robust Markov decision processes (RMDPs) --- optimize the worst-case performance when the deployed environment is within an uncertainty set around some nominal MDP. Despite recent efforts, the sample complexity of RMDPs has remained largely undetermined. While the statistical implications of distributional robustness in RL have been explored in some specific cases, the generalizability of the existing findings remains unclear, especially in comparison to standard RL. Assuming access to a generative model that samples from the nominal MDP, we examine the sample complexity of RMDPs using a class of generalized $L_p$ norms as the 'distance' function for the uncertainty set, under two commonly adopted $sa$-rectangular and $s$-rectangular conditions. Our results imply that RMDPs can be more sample-efficient to solve than standard MDPs using generalized $L_p$ norms in both $sa$- and $s$-rectangular cases, potentially inspiring more empirical research. We provide a near-optimal upper bound and a matching minimax lower bound for the $sa$-rectangular scenarios. For $s$-rectangular cases, we improve the state-of-the-art upper bound and also derive a lower bound using $L_\infty$ norm that verifies the tightness.

Safe reinforcement learning (RL) is crucial for deploying RL agents in real-world applications, as it aims to maximize long-term rewards while satisfying safety constraints. However, safe RL often suffers from sample inefficiency, requiring extensive interactions with the environment to learn a safe policy. We propose Efficient Safe Policy Optimization (ESPO), a novel approach that enhances the efficiency of safe RL through sample manipulation. ESPO employs an optimization framework with three modes: maximizing rewards, minimizing costs, and balancing the trade-off between the two. By dynamically adjusting the sampling process based on the observed conflict between reward and safety gradients, ESPO theoretically guarantees convergence, optimization stability, and improved sample complexity bounds. Experiments on the Safety-MuJoCo and Omnisafe benchmarks demonstrate that ESPO significantly outperforms existing primal-based and primal-dual-based baselines in terms of reward maximization and constraint satisfaction. Moreover, ESPO achieves substantial gains in sample efficiency, requiring 25--29\% fewer samples than baselines, and reduces training time by 21--38\%.

Offline model-based reinforcement learning (MBRL) enhances data efficiency by utilizing pre-collected datasets to learn models and policies, especially in scenarios where exploration is costly or infeasible. Nevertheless, its performance often suffers from the objective mismatch between model and policy learning, resulting in inferior performance despite accurate model predictions. This paper first identifies the primary source of this mismatch comes from the underlying confounders present in offline data for MBRL. Subsequently, we introduce **B**ilin**E**ar **CAUS**al r**E**presentation (BECAUSE), an algorithm to capture causal representation for both states and actions to reduce the influence of the distribution shift, thus mitigating the objective mismatch problem. Comprehensive evaluations on 18 tasks that vary in data quality and environment context demonstrate the superior performance of BECAUSE over existing offline RL algorithms. We show the generalizability and robustness of BECAUSE under fewer samples or larger numbers of confounders. Additionally, we offer theoretical analysis of BECAUSE to prove its error bound and sample efficiency when integrating causal representation into offline MBRL. See more details in our project page: [https://sites.google.com/view/be-cause](https://sites.google.com/view/be-cause).

This paper concerns the central issues of model robustness and sample efficiency in offline reinforcement learning (RL), which aims to learn to perform decision making from history data without active exploration. Due to uncertainties and variabilities of the environment, it is critical to learn a robust policy---with as few samples as possible---that performs well even when the deployed environment deviates from the nominal one used to collect the history dataset. We consider a distributionally robust formulation of offline RL, focusing on tabular robust Markov decision processes with an uncertainty set specified by the Kullback-Leibler divergence in both finite-horizon and infinite-horizon settings. To combat with sample scarcity, a model-based algorithm that combines distributionally robust value iteration with the principle of pessimism in the face of uncertainty is proposed, by penalizing the robust value estimates with a carefully designed data-driven penalty term. Under a mild and tailored assumption of the history dataset that measures distribution shift without requiring full coverage of the state-action space, we establish the finite-sample complexity of the proposed algorithms. We further develop an information-theoretic lower bound, which suggests that learning RMDPs is at least as hard as the standard MDPs when the uncertainty level is sufficient small, and corroborates the tightness of our upper bound up to polynomial factors of the (effective) horizon length for a range of uncertainty levels. To the best our knowledge, this provides the first provably near-optimal robust offline RL algorithm that learns under model uncertainty and partial coverage.

Robustness has been extensively studied in reinforcement learning (RL) to handle various forms of uncertainty such as random perturbations, rare events, and malicious attacks. In this work, we consider one critical type of robustness against spurious correlation, where different portions of the state do not have correlations induced by unobserved confounders. These spurious correlations are ubiquitous in real-world tasks, for instance, a self-driving car usually observes heavy traffic in the daytime and light traffic at night due to unobservable human activity. A model that learns such useless or even harmful correlation could catastrophically fail when the confounder in the test case deviates from the training one. Although motivated, enabling robustness against spurious correlation poses significant challenges since the uncertainty set, shaped by the unobserved confounder and causal structure, is difficult to characterize and identify. Existing robust algorithms that assume simple and unstructured uncertainty sets are therefore inadequate to address this challenge. To solve this issue, we propose Robust State-Confounded Markov Decision Processes (RSC-MDPs) and theoretically demonstrate its superiority in avoiding learning spurious correlations compared with other robust RL counterparts. We also design an empirical algorithm to learn the robust optimal policy for RSC-MDPs, which outperforms all baselines in eight realistic self-driving and manipulation tasks.

This paper investigates model robustness in reinforcement learning (RL) via the framework of distributionally robust Markov decision processes (RMDPs). Despite recent efforts, the sample complexity of RMDPs is much less understood regardless of the uncertainty set in use; in particular, there exist large gaps between existing upper and lower bounds, and it is unclear if distributional robustness bears any statistical implications when benchmarked against standard RL. In this paper, assuming access to a generative model, we derive the sample complexity of RMDPs---when the uncertainty set is measured via either total variation or $\chi^2$ divergence over the full range of uncertainty levels---using a model-based algorithm called distributionally robust value iteration, and develop minimax lower bounds to benchmark its tightness. Our results not only strengthen the prior art in both directions of upper and lower bounds, but also deliver surprising messages that learning RMDPs is not necessarily easier or more difficult than standard MDPs. In the case of total variation, we establish the minimax-optimal sample complexity of RMDPs which is always smaller than that of standard MDPs. In the case of $\chi^2$ divergence, we establish the sample complexity of RMDPs that is tight up to polynomial factors of the effective horizon, and grows linearly with respect to the uncertainty level when it approaches infinity.

Transformers hold tremendous promise in solving offline reinforcement learning (RL) by formulating it as a sequence modeling problem inspired by language modeling (LM). Prior works using transformers model a sample (trajectory) of RL as one sequence analogous to a sequence of words (one sentence) in LM, despite the fact that each trajectory includes tokens from three diverse modalities: state, action, and reward, while a sentence contains words only. Rather than taking a modality-agnostic approach which uniformly models the tokens from different modalities as one sequence, we propose a multimodal sequence modeling approach in which a trajectory (one “sentence”) of three modalities (state, action, reward) is disentangled into three unimodal ones (three “sentences”). We investigate the correlation of different modalities during sequential decision-making and use the insights to design a multimodal transformer, named Decision Transducer (DTd). DTd outperforms prior art in offline RL on the conducted D4RL benchmarks and enjoys better sample efficiency and algorithm flexibility. Our code is made publicly here.

Offline or batch reinforcement learning seeks to learn a near-optimal policy using history data without active exploration of the environment. To counter the insufficient coverage and sample scarcity of many offline datasets, the principle of pessimism has been recently introduced to mitigate high bias of the estimated values. While pessimistic variants of model-based algorithms (e.g., value iteration with lower confidence bounds) have been theoretically investigated, their model-free counterparts — which do not require explicit model estimation — have not been adequately studied, especially in terms of sample efficiency. To address this inadequacy, we study a pessimistic variant of Q-learning in the context of finite-horizon Markov decision processes, and characterize its sample complexity under the single-policy concentrability assumption which does not require the full coverage of the state-action space. In addition, a variance-reduced pessimistic Q-learning algorithm is proposed to achieve near-optimal sample complexity. Altogether, this work highlights the efficiency of model-free algorithms in offline RL when used in conjunction with pessimism and variance reduction.

Curriculum Reinforcement Learning (CRL) aims to create a sequence of tasks, starting from easy ones and gradually learning towards difficult tasks. In this work, we focus on the idea of framing CRL as interpolations between a source (auxiliary) and a target task distribution. Although existing studies have shown the great potential of this idea, it remains unclear how to formally quantify and generate the movement between task distributions. Inspired by the insights from gradual domain adaptation in semi-supervised learning, we create a natural curriculum by breaking down the potentially large task distributional shift in CRL into smaller shifts. We propose GRADIENT which formulates CRL as an optimal transport problem with a tailored distance metric between tasks. Specifically, we generate a sequence of task distributions as a geodesic interpolation between the source and target distributions, which are actually the Wasserstein barycenter. Different from many existing methods, our algorithm considers a task-dependent contextual distance metric and is capable of handling nonparametric distributions in both continuous and discrete context settings. In addition, we theoretically show that GRADIENT enables smooth transfer between subsequent stages in the curriculum under certain conditions. We conduct extensive experiments in locomotion and manipulation tasks and show that our proposed GRADIENT achieves higher performance than baselines in terms of learning efficiency and asymptotic performance.

We address the problem of enabling two-dimensional digital image correlation (DIC) for strain measurement on large three-dimensional objects with curved surfaces. It is challenging to acquire full-field qualified images of the surface required by DIC due to geometric distortion and the narrow visual field of the surface that a single image can cover. To overcome this issue, we propose an end-to-end DIC framework incorporating the image fusion principle to achieve full-field strain measurement over the curved surface. With a sequence of blurry images as inputs, we first recover sharp images using blind deconvolution, then project recovered sharp images to the curved surface using camera poses estimated by our proposed perspective-n-point (PnP) method called RRWLM. Images on the curved surface are stitched and then unfolded for strain analysis using DIC. Numerical experiments are conducted to validate our framework using RRWLM with comparisons to existing methods.

Camera pose estimation plays a crucial role in stitching overlapped images captured by a camera to achieve a broad view of interest. In this paper, we propose a robust camera pose estimation approach to stitching images of a large 3D surface with known geometry. In particular, given a collection of images, we first construct a relative pose matrix estimation of all image pairs from the collection, where each entry of the matrix is calculated by solving a perspective-n-point (PnP) problem over the corresponding pair of images. To continue, we jointly estimate all camera poses by solving an optimization problem that exploits the underlying rank-2 relative pose matrices and the joint sparsity of camera pose errors. Finally, images are projected on to the 3D surface of interest based on estimated camera poses for the subsequent stitching process. Numerical experiments demonstrate that our proposed method outperforms existing methods in terms of both camera pose estimation and image stitching quality.

Achieving sample efficiency in online episodic reinforcement learning (RL) requires optimally balancing exploration and exploitation. When it comes to a finite-horizon episodic Markov decision process with $S$ states, $A$ actions and horizon length $H$, substantial progress has been achieved towards characterizing the minimax-optimal regret, which scales on the order of $\sqrt{H^2SAT}$ (modulo log factors) with $T$ the total number of samples. While several competing solution paradigms have been proposed to minimize regret, they are either memory-inefficient, or fall short of optimality unless the sample size exceeds an enormous threshold (e.g., $S^6A^4 \,\mathrm{poly}(H)$ for existing model-free methods).To overcome such a large sample size barrier to efficient RL, we design a novel model-free algorithm, with space complexity $O(SAH)$, that achieves near-optimal regret as soon as the sample size exceeds the order of $SA\,\mathrm{poly}(H)$. In terms of this sample size requirement (also referred to the initial burn-in cost), our method improves --- by at least a factor of $S^5A^3$ --- upon any prior memory-efficient algorithm that is asymptotically regret-optimal. Leveraging the recently introduced variance reduction strategy (also called {\em reference-advantage decomposition}), the proposed algorithm employs an {\em early-settled} reference update rule, with the aid of two Q-learning sequences with upper and lower confidence bounds. The design principle of our early-settled variance reduction method might be of independent interest to other RL settings that involve intricate exploration-exploitation trade-offs.

Multi-channel sparse blind deconvolution, or convolutional sparse coding, refers to the problem of learning an unknown filter by observing its circulant convolutions with multiple input signals that are sparse. This problem finds numerous applications in signal processing, computer vision, and inverse problems. However, it is challenging to learn the filter efficiently due to the bilinear structure of the observations with respect to the unknown filter and inputs, as well as the sparsity constraint. In this paper, we propose a novel approach based on nonconvex optimization over the sphere manifold by minimizing a smooth surrogate of the sparsity-promoting loss function. It is demonstrated that manifold gradient descent with random initializations will probably recover the filter, up to scaling and shift ambiguity, as soon as the number of observations is sufficiently large under an appropriate random data model. Numerical experiments are provided to illustrate the performance of the proposed method with comparisons to existing ones.

Multi-channel sparse blind deconvolution refers to the problem of learning an unknown filter by observing its circulant convolutions with multiple input signals that are sparse. It is challenging to learn the filter efficiently due to the bilinear structure of the observations with respect to the unknown filter and inputs, leading to global ambiguities of identification. We propose a novel approach based on nonconvex optimization over the sphere manifold by minimizing a smooth surrogate of the sparsity-promoting loss function. It is demonstrated that manifold gradient descent with random initializations provably recovers the filter, up to scaling and shift ambiguities, as soon as the number of observations is sufficiently large under a suitable random data model. Numerical experiments are conducted to illustrate the efficiency of the proposed method with comparisons to existing methods.