Markov Decision Processes

Inpatient clinical reasoning is a sequential decision under partial observability: the clinician sees the admission so far and must choose the next action whose downstream consequences are not yet visible. Existing clinical-LLM evaluations and RL rewards signals collapse this into closed-form retrieval, clinical journey leakage, or unanchored LLM-as-judge scoring. We introduce CLR-voyance, a framework that reformulates inpatient reasoning as a Partially Observable Markov Decision Process (POMDP) and supervises it with rewards that are simultaneously outcome-grounded and clinician-validated. We instantiate the formulation as CLR-POMDP, which partitions successful patient journeys into a policy-visible past and an oracle-only future. Using the past information, an oracle LLM generates a case-specific query-answer pair, and the first adaptive rubric for clinical reasoning which is verifiable in the future of the patient journey. These rubrics are used for both post-training and evaluation of models for inpatient clinical reasoning. We post-train Qwen3-8B and MedGemma-4B with GRPO followed by model merging, yielding state-of-the-art inpatient clinical reasoning while retaining generalist capabilities. CLR-voyance-8B achieves 84.91% on CLR-POMDP, ahead of frontier medical reasoning models like GPT-5 (77.83%) and MedGemma-27B (66.66%) and has comparable or better performance on existing medical benchmarks. To ensure a clinically meaningful setting, we conduct a large-scale clinician alignment study, where physicians curate per-case rubrics, grade candidate responses, and provide blinded pairwise preferences of model reasoning. This study provides insights on clinical LLM-as-a-judge and clinical preference-model selection, which can inform the community at large. CLR-voyance has been deployed for 6+ months at a partner public hospital, drafting thousands of reasoning-heavy inpatient notes.

Large language models (LLMs) have shown remarkable in-context learning (ICL) capabilities, yet their potential for sequential decision-making remains underexplored. In this paper, we study the ICL capabilities of LLMs in sequential decision-making settings, including Markov Decision Processes (MDPs), Partially Observable MDPs (POMDPs), and Ambiguous POMDPs (APOMDPs). We fine-tune pretrained LLMs to perform few-shot decision-making directly from offline, oracle-labeled trajectories. Our framework enables flexible imitation of policies through supervised fine-tuning (SFT). Theoretically, we focus on linear MDPs and interpret a fine-tuned attention layer as implicitly estimating optimal Q-functions from in-context data. Building on this interpretation, we derive an end-to-end suboptimality bound for the induced policy that separates the in-context estimation error from the training-length bias. Empirically, across synthetic MDP, POMDP, and APOMDP settings, we find that fine-tuned LLMs achieve substantially smaller optimality gaps than in-context-only and random baselines, with especially large gains in longer-horizon, partially observed, and model-ambiguous environments. Together, these results show that supervised fine-tuning provides an effective route to endowing pretrained LLMs with sequential decision-making capabilities from offline data, which is an important advantage in domains such as healthcare where offline data are abundant.

Preference-conditioned multi-objective reinforcement learning aims to learn a single policy that captures trade-offs across preferences, but under nonlinear scalarization the uniqueness and continuity of the preference-to-solution correspondence remain unclear. We study this problem in tabular multi-objective Markov decision processes (MDPs) using smooth Tchebycheff scalarization as a monotone utility. Under mild interior conditions on the preference set, we prove that each preference induces a unique Pareto-optimal return vector and that this vector depends Lipschitz-continuously on the preference, providing a principled foundation for preference sweeping toward dense Pareto-front coverage. To compute these targets, we formulate the problem over occupancy measures and derive Concave Mirror Descent Policy Iteration (CMDPI), which achieves an $O(1/k)$ objective-suboptimality rate. We further show that each update is equivalent to solving a Kullback-Leibler-regularized MDP with the previous policy as reference, yielding a policy-iteration interpretation and finite-iterate policy continuity across preferences. We instantiate the update as a deep actor-critic algorithm preserving previous-policy regularization. On eight MO-Gymnasium tasks, it achieves the best average hypervolume rank among recent baselines and strong expected-utility performance. Continuous-control experiments indicate gains beyond the discrete-action setting.

Reinforcement learning (RL) for exponential-utility optimization in discounted Markov decision processes (MDPs) lacks principled value-based algorithms. We address this gap in the fixed risk-aversion setting. Building on the Bellman-type equation for exponential utility studied in \cite{porteus1975optimality}, we derive two Q-value-style extensions and show that the associated operators are contractions in the $L_\infty$ and sup-log/Thompson metrics, respectively. We characterize their fixed points and prove that the induced greedy stationary policy is optimal for the exponential-utility objective among stationary policies. These structural results lead to two model-free algorithms: a two-timescale Q-learning--style algorithm, for which we establish almost-sure convergence and provide finite-time convergence rates via timescale separation, and a one-timescale algorithm governed by a sublinear power-law operator. Since the latter does not admit a global contraction in standard metrics, we prove its convergence using delicate arguments based on local Lipschitzness, monotonicity, homogeneity, and Dini derivatives, and provide a scalar finite-time analysis that highlights the challenges in obtaining convergence rates in the vector case. Our work provides a foundation for value-based RL under exponential-utility objectives.

This paper presents a finite-time analysis for Monte Carlo Tree Search (MCTS) in Partially Observable Markov Decision Processes (POMDPs), with probabilistic concentration bounds in both discrete and continuous observation spaces. While MCTS-style solvers such as POMCP achieve empirical success in many applications, rigorous finite-time guarantees remain an open problem due to the nonstationarity and the interdependencies induced by heuristic action selection (e.g., UCB). In the discrete setting, we address these challenges by extending the polynomial exploration bonus to UCB in POMDP setting, yielding polynomial concentration bounds for the empirical value estimation at the root node. For continuous observation spaces, we introduce an abstract partitioning framework and propose a finite-time bound on partitioning loss. Under mild conditions, we prove highprobability bound on value estimates in POMDPs with continuous observation space. Specifically, we propose Voro-POMCPOW, a variant of POMCPOW with f inite-time guarantees that adaptively partitions the continuous observation space using Voronoi cells. This approach maintains a finite branching factor while preserving the original observation generator. Empirical validation demonstrates that the proposed Voro-POMCPOW shows competitive performance while providing theoretical guarantees. Although our analysis focuses on continuous POMDPs, the techniques developed herein are also applicable to continuous MDPs, closing another gap on the MDP side.

Partially Observable Markov Decision Processes (POMDPs) are systems in which one agent interacts with a stochastic environment, and receives only partial information about the current state. In a multi-environment POMDP (MEPOMDP), the initial state is unknown, and assumed to be adversarially chosen. In this work we focus on computing the optimal value and policy in MEPOMDPs with finite-horizon objectives. That problem is known to be PSPACE-complete in POMDPs. Our main results are as follows: (1) we establish that it is also PSPACE-complete in the more general setting of MEPOMDPs; (2) we present a practical algorithm and evaluate it on classical benchmarks, significantly outperforming the only previously known algorithm.

For continuous state-action space scenarios, classical reinforcement learning (RL) theory predominantly focuses on low-rank Markov decision processes (MDPs), which provide sample-efficient guarantees at the expense of restrictive structural assumptions. Kernel smoothing model-based approaches offer a promising alternative paradigm that instead leverages the smoothness of the MDP and employs non-parametric kernel smoothing estimates of transition dynamics. This paper proposes a new kernel-smoothing model-based approach for online reinforcement learning in finite-horizon settings under Lipschitz continuity assumptions on the MDP. By incorporating a Bernstein-style exploration bonus into the kernel smoothing framework, our method achieves a regret bound which improves upon the state-of-the-art regret bound in its dependence on the horizon. The theoretical advancement relies on a delicate analysis of the synergy between Bernstein-style bonuses and kernel smoothing, where a new tight Bernstein-type concentration inequality for martingales may be of independent interest.

Regulatory approval of products in high-stakes domains such as drug development requires statistical evidence of safety and efficacy through large-scale randomized controlled trials. However, the high financial cost of these trials may deter developers who lack absolute certainty in their product's efficacy, ultimately stifling the development of `moonshot' products that could offer high social utility. To address this inefficiency, in this paper, we introduce a statistical protocol for experimentation where the product developer (the agent) conducts a randomized controlled trial sequentially and the regulator (the principal) partially subsidizes its cost. By modeling the protocol using a belief Markov decision process, we show that the agent's optimal strategy can be found efficiently using dynamic programming. Further, we show that the social utility is a piecewise linear and convex function over the subsidy level the principal selects, and thus the socially optimal subsidy can also be found efficiently using divide-and-conquer. Simulation experiments using publicly available data on antibiotic development and approval demonstrate that our statistical protocol can be used to increase social utility by more than 35$$\% relative to standard, non-sequential protocols.

Online-safety regulation under the UK Online Safety Act and the EU Digital Services Act increasingly treats scalar metrics as compliance evidence. Once announced, such a metric also becomes an optimization target: a strategic platform can improve its score by routing recommendations through semantically equivalent content variants, without reducing true harm. We ask when such an audit metric can still certify a genuine reduction in harm. The protocol is modeled as a published transformation graph whose connected components form semantic classes, and the metric itself is treated as a security object. Three results follow. First, any metric that scores variants directly is manipulable as soon as two equivalent variants in a harmful class disagree in score. Second, the semantic-envelope lift, which assigns each variant the maximum score in its class, is the unique pointwise minimum among conservative classwise-constant repairs. Third, a class-stratified certificate, $H^\star(x) \le (1/\hatα) M_{\mathrm{Env}(m)}(x) + \barη$, holds for every platform strategy, with $\barη$ absorbing annotation and protocol error. We check the claims at three levels: exhaustive enumeration on a finite-state grid of mixed strategies, an SMT encoding in Z3 cross-replayed in cvc5, and a bounded single-player MDP encoded in PRISM-games. The fragile metric fails manipulation invariance and cannot support the same useful predeclared class-coverage certificate; under the envelope-level certificate, it produces large violations at every tested instance, with a large mean gaming gap across random catalogs at a fixed audit budget. The semantic-envelope metric exhibits no such violation in the tested instances.

Robots operate under significant uncertainty, from quantifiable noise to unquantifiable unknowns, and must account for strict operational constraints, such as limited resources. In this paper, we consider the problem of synthesizing robust strategies to guide a robot's actions in fulfilling a given task, while ensuring the system never exhausts its resources. To solve this problem, we first model the robotic system as a Consumption Markov Decision Process with Set-valued Transitions(CMDPST), a unified framework modelling nondeterministic actions, quantifiable and unquantifiable uncertainty, and resource consumption. Then, we combine the CMDPST with the task specification, expressed as a Linear Temporal Logic over finite traces (LTLf ) formula. Lastly, we address the resource constrained optimal robust strategy synthesis problem, which aims to synthesize a strategy that maximizes the probability of satisfying the LTLf objective without resource exhaustion. Our solution involves two techniques: a direct unrolling-based method and a more efficient, optimized approach that leverages state-space pruning for better performance. Experiments on a warehouse transportation network show the effectiveness of the proposed solutions.

While reinforcement learning (RL) promises to revolutionize the control of complex nonlinear robotic systems, a profound gap persists between the heuristic success of model-free off-policy deep RL and the underlying theory, which remains largely confined to tabular or linearizable settings. We identify the cause of this gap as an emergent isolation of three traditions: (i) measure-theoretic MDP foundations on general spaces limit their analysis to exact dynamic programming and ignore all error sources of a learning process; (ii) deterministic error propagation analysis addresses the approximation error via concentrability coefficients without a finite-sample analysis of the estimation error; and (iii) PAC generalization bounds characterize the estimation errors of simplified topologies. We bridge these traditions with a unified theoretical framework for fitted Q-iteration (FQI) on general measurable Borel spaces. Our main result provides a finite-sample, adaptive-data performance bound by chaining measure-theoretic probability with Bellman-operator contraction in Banach spaces. We prove that sequential Rademacher complexity controls Bellman-regression generalization under policy-dependent data collection. We further extend this analysis to provide the first cumulative, pathwise online regret guarantee for FQI in continuous spaces. These results lay the necessary foundations for the formal analysis of many modern deep RL algorithms.

A Tree Markov Decision Problem (T-MDP) is a finite-horizon MDP with a starting state $s_{1}$, in which every state is reachable from $s_{1}$ through exactly one state-action trajectory. T-MDPs arise naturally as abstractions of decision making in sequential games with perfect recall, against stationary opponents. We consider the problem of on-line learning in T-MDPs, both in the PAC and the regret-minimisation regimes. We show that well-known bandit algorithms -- \textsc{Lucb} and \textsc{Ucb} -- can be applied on T-MDPs by treating each policy as an arm. The apparent technical challenge in this approach is that the number of policies is exponential in the number of states. Our main innovation is in the design of confidence bounds based on data shared by the policies, so that the bandit algorithms can yet be implemented with polynomial memory and per-step computation. We obtain instance-dependent upper bounds on sample complexity and regret that sum a ``gap term'' from every terminal state, rather than every policy. Empirically, our algorithms consistently outperform available alternatives on a suite of hidden-information games.

Recent research has revived and amplified interest in algorithms for undiscounted average reward reinforcement learning in infinite-horizon, non-episodic (continuing) tasks. Semi-Markov decision processes (SMDPs) are of particular interest. In SMDPs, discrete actions stochastically generate both rewards and durations, and the objective is to optimize the average reward rate. Existing algorithms approach this by optimizing the ratio of rewards to durations. However, when rewards and durations are non-stationary (in the infinite horizon), this can be incorrect. This paper presents a novel modified harmonic mean operator that correctly computes reward rates even under such conditions. This yields model-free learning algorithms that can work with SMDPs, while maintaining robustness to non-stationary reward and duration distributions over time. We prove theoretical properties of the modified harmonic mean operator, and empirically demonstrate its efficacy in comparison to existing algorithms.

We study the $(\varepsilon, δ)$-PAC policy identification problem in finite-horizon episodic Markov Decision Processes. Existing approaches provide finite-time guarantees for approximate settings ($\varepsilon>0$) but suffer from high computational cost, rendering them hard to implement, and also suffer from suboptimal dependence on $\log(1/δ)$. We propose a randomized and computationally efficient algorithm for best policy identification that combines posterior sampling with an online learning algorithm to guide exploration in the MDP. Our method achieves asymptotic optimality in sample complexity, also in terms of posterior contraction rate, and runs in $O(S^2AH)$ per episode, matching standard model-based approaches. Unlike prior algorithms such as MOCA and PEDEL, our guarantees remain meaningful in the asymptotic regime and avoid sub-optimal polynomial dependence on $\log(1/δ)$. Our results provide both theoretical insights and practical tools for efficient policy identification in tabular MDPs.

Contextual MDPs are powerful tools with wide applicability in areas from biostatistics to machine learning. However, specializing them to offline datasets has been challenging due to a lack of robust, theoretically backed methods. Our work tackles this problem by introducing a new approach towards adaptive estimation and cost optimization of contextual MDPs. This estimator, to the best of our knowledge, is the first of its kind, and is endowed with strong optimality guarantees. We achieve this by overcoming the key technical challenges evolving from the endogenous properties of contextual MDPs; such as non-stationarity, or model irregularity. Our guarantees are established under complete generality by utilizing the relatively recent and powerful statistical technique of $T$-estimation (Baraud, 2011). We first provide a procedure for selecting an estimator given a sample from a contextual MDP and use it to derive oracle risk bounds under two distinct, but nevertheless meaningful, loss functions. We then consider the problem of determining the optimal control with the aid of the aforementioned density estimate and provide finite sample guarantees for the cost function.

Multi-agent reinforcement learning (MARL) holds great potential but faces robustness challenges due to environmental uncertainty. To address this, distributionally robust Markov games (RMGs) optimize worst-case performance when the environment deviates from the nominal model within a uncertainty set. Beyond robustness, an equally urgent goal for MARL is data efficiency -- sampling from vast state and action spaces that grow exponentially with the number of agents potentially leads to the curse of multiagency. However, current provably data-efficient algorithms for RMGs are limited to tabular settings with finite state and action spaces, which are only computationally manageable for small-scale problems, leaving RMGs with large-scale (or infinite) state spaces largely unexplored. The only existing work beyond tabular settings focuses on linear function approximation (LFA) for a restrictive class of RMGs using vanish minimal value assumption and still suffers from sample complexity with the curse of multiagency. In this work, we focuses on general RMGs with LFA. For uncertainty sets defined by total variation distance, we develop provably data-efficient algorithms that break the curse of multiagency in both the generative model setting and a newly proposed online interactive setting. To our knowledge, our results are the first to break the curse of multiagency of sample complexity for RMGs with large (possibly infinite) state spaces, regardless of the uncertainty set construction.

Middle-mile logistics describes the problem of routing parcels through a network of hubs linked by trucks with finite capacity. We rephrase this as a multi-object goal-conditioned MDP. Our method combines graph neural networks with model-free RL, extracting small feature graphs from the environment state.

This paper develops a deep reinforcement learning based observer control policy for autonomous bearings-only tracking of a moving target. The observer manoeuvre problem is formulated as a belief Markov decision process, where the belief state is represented by the posterior of a cubature Kalman filter (CKF). The reward function is designed to address two conflicting objectives: minimising the absolute target position estimation error (Euclidean distance) and maintaining CKF estimation consistency (Mahalanobis distance). The reward is formulated as a geometric interpolation between the two objectives on the Pareto front, parametrised by a weighting factor $β\in [0,1]$. The policy is implemented as a deep Q-network (DQN) trained over 50,000 episodes. Performance is evaluated over 5,000 Monte Carlo episodes and compared against two baselines: the perpendicular-to-bearing heuristic and the D-optimal Fisher information maximisation criterion. The results show that the DQN policy at $β= 0.7$ achieves the best trade-off between accuracy and robustness: it matches the information-theoretic baseline on mean tracking accuracy while reducing the worst-case error by nearly a factor of ten, owing to the implicit filter-consistency regularisation provided by the Mahalanobis term in the reward.

Learning-based approaches to verifying unknown Markov decision processes (MDPs) often employ uncertain MDPs. These models use, for example, confidence intervals to capture transition uncertainty and allow synthesis of policies that are robust to this uncertainty. However, this approach typically quantifies uncertainty independently for individual transition probabilities, ignoring dependencies due to shared latent quantities. We propose to learn such models using parametric MDPs (pMDPs), where transition probabilities are expressions over a set of parameters. We project statistical uncertainty from empirical transition frequencies onto the pMDP's parameter space, yielding a probably approximately correct (PAC) uncertainty model for the underlying MDP that respects the algebraic dependencies between transitions. The resulting models are algorithmically challenging to solve, so we propose a hierarchy of sound polytopic outer approximations of the induced confidence set. We implement and evaluate our approach, demonstrating substantially tighter uncertainty estimates than classical interval-based uncertain MDP learning techniques.

Reinforcement learning (RL) is a fundamental framework for sequential decision-making, in which an agent learns an optimal policy through interactions with an unknown environment. In settings with function approximation, many existing RL algorithms achieve favorable sample complexity, but often rely on computationally intractable oracles. In this paper, we use supervised learning as a computational proxy to establish a clear hierarchy of commonly adopted RL oracles under low-rank Markov Decision Processes (MDPs). This hierarchy shows that policy evaluation is the most computationally efficient oracle, provided that supervised learning can be efficiently solved. Motivated by this observation, we propose a novel optimistic actor-critic algorithm that relies solely on the policy evaluation oracle. We prove that our algorithm outperforms the existing sample complexity guarantees for low-rank MDPs while avoiding computationally expensive planning or optimization oracles commonly assumed in prior works. We further extend our theoretical results to approximately low-rank MDPs and demonstrate that this setting captures a broad class of real-world environments. Finally, we validate our theoretical results with experiments on several standard Gym environments.

Reinforcement learning (RL) in large environments often suffers from severe computational bottlenecks, as conventional regret minimization algorithms require repeated, costly calls to planning and statistical estimation oracles. While recent advances have explored offline oracle-efficient algorithms, their computational complexity typically scales with the cardinality of the state and action spaces, rendering them intractable for large-scale or continuous environments. In this paper, we address this fundamental limitation by studying offline oracle-efficient episodic RL through the lens of log-barrier and log-determinant regularization. Specifically, for tabular Markov Decision Processes (MDPs), we propose a novel algorithm that achieves the optimal $\tilde{O}(\sqrt{T})$ regret bound while requiring only $O(H\log\log T)$ calls to both the offline statistical estimation and planning oracles when $T$ is known and $O(H\log T)$ calls when $T$ is unknown. Crucially, this oracle complexity is entirely independent of the size of the state and action spaces. This strict independence drastically reduces the planning oracle complexity, representing a substantial improvement over existing offline oracle-efficient algorithms (Qian et al., 2024). Furthermore, we demonstrate the versatility of our framework by generalizing the algorithm to linear MDPs featuring infinite state spaces and arbitrary action spaces. We prove that this generalized approach successfully attains meaningful sub-linear regret. Consequently, our work yields the first doubly oracle-efficient (i.e., efficient with respect to both statistical estimation and policy optimization) regret minimization algorithm capable of solving MDPs with infinite state and action spaces, significantly expanding the boundaries of computationally tractable RL.

Deploying reinforcement learning policies in the real world requires adapting to time-varying environments. We study this problem in the contextual Markov Decision Process (cMDP) framework, where a family of environments is indexed by a low-dimensional context unknown at test time. The standard approach decomposes the problem: train a so-called "universal policy" which assumes knowledge of the true context, then pair it with a context estimator which approximates context using the observed trajectory. We identify a simple, counterintuitive trick that substantially improves the estimator: randomly delete a fraction of the training buffer after each round. This works because data is collected across multiple rounds using progressively better policies, and older trajectories come from a different distribution than what the estimator will face at deployment time; random deletion creates an implicit exponential decay on older data while preserving diversity without requiring any explicit identification of which samples are stale. This reduces robustness gap by 30% for MLPs and by 6% on average for recurrent networks. Strikingly, it allows a narrow MLP with 5x fewer parameters to outperform a wide MLP trained without deletion. To understand when and why deletion helps, we analyze regularized empirical risk minimization with a mismatch between the train distribution and the distribution at deployment; in this idealized setting, we prove that removing a single uniformly random training point decreases expected test loss in expectation under mild conditions. For ridge regression we make this quantitative: deletion helps when the regularization coefficient is moderate and the signal-to-noise ratio (SNR) is sufficiently low, and, crucially, this SNR threshold gives a direct measure of how large the distribution mismatch between training and deployment must be for deletion to be beneficial.

Electric truck operations require routing decisions that remain feasible under limited battery range, long charging times, travel and energy consumption, and competition for shared charging infrastructure. These features make electric truck routing a coupled logistics and energy problem, limiting the practicality of heuristics-based methods and rendering them computationally infeasible at scale. This paper proposes a learning-based framework for the stochastic electric truck routing under charging constraints and operational uncertainty. The problem, solved by Reinforcement Learning, is formulated as an event-driven semi-Markov decision process with shared charging resources, stochastic travel and energy requirements, and realistic nonlinear fast-charging behavior. To support learning in this setting, a graph-based representation of system state and feasible decisions is introduced, together with a rule-based action mask that restricts policies to operationally admissible actions; thus, improving training efficiency. Building on this formulation, an event-driven simulation environment is developed that supports both Reinforcement Learning and benchmarking against heuristic and mathematical programming baselines. Computational experiments across a range of fleet sizes show that the proposed learning-based algorithm consistently outperforms baselines and attains performance close to optimization benchmarks in many settings, while preserving high success rates under charging congestion and uncertainty.

We study city-scale control of electric-vehicle (EV) ride-hailing fleets where dispatch, repositioning, and charging decisions must respect charger and feeder limits under uncertain, spatially correlated demand and travel times. We formulate the problem as a hex-grid semi-Markov decision process (semi-MDP) with mixed actions -- discrete actions for serving, repositioning, and charging, together with continuous charging power -- and variable action durations. To guarantee physical feasibility during both training and deployment, the policy learns over high-level intentions produced by a masked, temperature-annealed actor. These intentions are projected at every decision step through a time-limited rolling mixed-integer linear program (MILP) that strictly enforces state-of-charge, port, and feeder constraints. To mitigate distributional shifts, we optimize a Soft Actor-Critic (SAC) agent against a Wasserstein-1 ambiguity set with a graph-aligned Mahalanobis ground metric that captures spatial correlations. The robust backup uses the Kantorovich-Rubinstein dual, a projected subgradient inner loop, and a primal-dual risk-budget update. Our architecture combines a two-layer Graph Convolutional Network (GCN) encoder, twin critics, and a value network that drives the adversary. Experiments on a large-scale EV fleet simulator built from NYC taxi data show that PD-RSAC achieves the highest net profit, reaching $1.22M, compared with $0.58M-$0.70M for strong heuristic, single-agent RL, and multi-agent RL baselines, including Greedy, SAC, MAPPO, and MADDPG, while maintaining zero feeder-limit violations.

Aligning denoising generative models with human preferences or verifiable rewards remains a key challenge. While policy-gradient online reinforcement learning (RL) offers a principled post-training framework, its direct application is hindered by the intractable likelihoods of these models. Prior work therefore either optimizes an induced Markov decision process (MDP) over sampling trajectories, which is stable but inefficient, or uses likelihood surrogates based on the diffusion evidence lower bound (ELBO), which have so far underperformed on visual generation. Our key insight is that the ELBO-based approach can, in fact, be made both stable and efficient. By reducing surrogate variance and controlling gradient steps, we show that this approach can beat MDP-based methods. To this end, we introduce Variational GRPO (V-GRPO), a method that integrates ELBO-based surrogates with the Group Relative Policy Optimization (GRPO) algorithm, alongside a set of simple yet essential techniques. Our method is easy to implement, aligns with pretraining objectives, and avoids the limitations of MDP-based methods. V-GRPO achieves state-of-the-art performance in text-to-image synthesis, while delivering a $2\times$ speedup over MixGRPO and a $3\times$ speedup over DiffusionNFT.

Here, we explore the problem of error propagation mitigation in modular digital twins as a sequential decision process. Building on a companion study that used a Hidden Markov Model (HMM) to infer latent error regimes from surrogate-physics residuals, we develop a Markov Decision Process (MDP) in which the inferred regimes serve as states, corrective interventions serve as actions, and a scalar reward that takes into consideration the cost-benefit tradeoff between system fidelity and maintenance expense. The baseline transition matrix is extracted from the HMM-learned parameters. We then extend the formulation to a Partially Observable MDP (POMDP) that accounts for the imperfect nature of regime classification by maintaining a belief distribution updated via Bayesian filtering, with the HMM confusion matrix serving as the observation model. Both formulations are solved via dynamic programming and validated through Gillespie stochastic simulation. We then benchmark two model-free reinforcement learning algorithms, Q-learning and REINFORCE, to assess whether effective policies can be learned without explicit model knowledge. A systematic comparison of different intervention policies demonstrates that the MDP policy achieves the highest cumulative reward and fraction of time in nominal operation, while the POMDP recovers approximately 95% of MDP performance under realistic observation noise. Sensitivity analyses across observation quality, repair probability, and discount factor confirm the robustness of these conclusions, and the major gaps in the policy hierarchy are statistically significant at $p < 0.001$. The gap between MDP and POMDP performance quantifies the value of information providing a principled criterion for investing in improved classification accuracy.

Autonomous systems that rely on learned perception can make unsafe decisions when sensor readings are misclassified. We study shielding for this setting: given a proposed action, a shield blocks actions that could violate safety. We consider the common case where system dynamics are known but perception uncertainty must be estimated from finite labeled data. From these data we build confidence intervals for the probabilities of perception outcomes and use them to model the system as a finite Interval Partially Observable Markov Decision Process with discrete states and actions. We then propose an algorithm to compute a conservative set of beliefs over the underlying state that is consistent with the observations seen so far. This enables us to construct a runtime shield that comes with a finite-horizon guarantee: with high probability over the training data, if the true perception uncertainty rates lie within the learned intervals, then every action admitted by the shield satisfies a stated lower bound on safety. Experiments on four case studies show that our shielding approach (and variants derived from it) improves the safety of the system over state-of-the-art baselines.

We propose SmoothCruiser, a new planning algorithm for estimating the value function in entropy-regularized Markov decision processes and two-player games, given a generative model of the environment. SmoothCruiser makes use of the smoothness of the Bellman operator promoted by the regularization to achieve problem-independent sample complexity of order O~(1/epsilon^4) for a desired accuracy epsilon, whereas for non-regularized settings there are no known algorithms with guaranteed polynomial sample complexity in the worst case.

High-fidelity measurements of continuum physical fields are essential for scientific discovery and engineering design but remain challenging under sparse and constrained sensing. Conventional reconstruction methods typically rely on fixed sensor layouts, which cannot adapt to evolving physical states. We propose LASER, a unified, closed-loop framework that formulates active sensing as a Partially Observable Markov Decision Process (POMDP). At its core, LASER employs a continuum field latent world model that captures the underlying physical dynamics and provides intrinsic reward feedback. This enables a reinforcement learning policy to simulate ''what-if'' sensing scenarios within a latent imagination space. By conditioning sensor movements on predicted latent states, LASER navigates toward potentially high-information regions beyond current observations. Our experiments demonstrate that LASER consistently outperforms static and offline-optimized strategies, achieving high-fidelity reconstruction under sparsity across diverse continuum fields.

Safe Reinforcement Learning from Human Feedback (Safe RLHF) has recently achieved empirical success in developing helpful and harmless large language models by decoupling human preferences regarding helpfulness and harmlessness. Existing approaches typically rely on fitting fixed horizon reward models from human feedback and have only been validated empirically. In this paper, we formulate safe RLHF as an infinite horizon discounted Con- strained Markov Decision Process (CMDP), since humans may interact with the model over a continuing sequence of interactions rather than within a single finite episode. We propose two Safe RLHF algorithms that do not require reward model fitting and, in contrast to prior work assuming fixed-length trajectories, support flexible trajectory lengths for training. Both algo- rithms are based on the primal-dual method and achieve global convergence guarantees with polynomial rates in terms of policy gradient iterations, trajectory sample lengths, and human preference queries. To the best of our knowledge, this is the first work to study infinite horizon discounted CMDP under human feedback and establish global, non-asymptotic convergence.

Agentic reinforcement learning (RL) is emerging as a critical post-training paradigm for improving LLM agent capabilities. Existing RL algorithms for LLMs largely follow the token-centric paradigm as in RLHF and RLVR, where tokens serve as the basic units for modeling and optimization. However, this paradigm introduces a granularity mismatch in agentic RL, as it optimizes token-level predictions while LLM agents make step-level decisions through cycles of environmental observations and actions. To bridge this gap, we propose \textbf{StepPO}, a step-centric paradigm for agentic RL via step-aligned policy optimization. Specifically, we reformulate agentic RL from a token-level Markov Decision Process (MDP) into a step-level MDP, where interaction steps serve as the basic trajectory representations. We further propose step-level credit assignment to align policy optimization with the natural granularity of agent decisions. Together, StepPO optimizes agent policies at the step level for multi-turn agent-environment interaction. Experiments across multi-hop QA, academic paper search, and text-world action tasks show that StepPO consistently outperforms various RL algorithms. Further analyses provide insights into how step-centric paradigm improves agent training. We hope this step-centric paradigm offers a useful lens for understanding agent behavior and a practical path for training more capable LLM agents.

Off-policy learning in constrained MDPs with large binary state spaces faces a fundamental tension: causal identification of transition dynamics requires structural assumptions, while sample-efficient policy learning requires state-space compression. We introduce PI-CMDP, a framework for CMDPs whose constraint dependencies form a layered DAG under a Lifecycle Ordering Assumption (LOA). We propose an Identify-Compress-Estimate pipeline: (i) Identify: LOA enables backdoor identification of causal edge weights for cross-layer pairs, with formal partial-identification bounds when LOA is violated; (ii) Compress: a Markov abstraction compresses state cardinality from 2^(WL) to (W+1)^L under layer-priority regularity and exchangeability; and (iii) Estimate: a physics-guided doubly-robust estimator remains unbiased and reduces the variance constant when the physics prior outperforms a learned model. We instantiate PI-CMDP on constraint repair in engineering simulation pipelines. On the TPS benchmark (4,206 episodes), PI-CMDP achieves 76.2% repair success rate with only 300 training episodes versus 70.8% for the strongest baseline (+5.4 pp), narrowing to +2.8 pp (83.4% vs. 80.6%) in the full-data regime, while substantially reducing cascade failure rates. All improvements are consistent across 5 independent seeds (paired t-test p < 0.02).

We study model-free reinforcement learning (RL) in non-stationary finite-horizon episodic Markov decision processes (MDPs) without prior knowledge of the non-stationarity. We focus on the piecewise stationary (PS) setting, where both rewards and transition dynamics can change at unknown times. We first revisit existing state-of-the-art approaches and identify theoretical and practical limitations that change the current landscape of performance guarantees. To characterize the difficulty of the problem, we establish the first minimax lower bounds for PS-RL in tabular and linear MDPs. We then introduce Detection Augmented Reinforcement Learning (DARLING), a modular wrapper for PS-RL that applies to both tabular and linear MDPs, without knowledge of the changes. In tabular MDPs, under change-point separability and reachability conditions, DARLING improves the best known dynamic regret bounds and matches our minimax lower bound. In linear MDPs, DARLING matches the minimax lower bound when the relevant reachability parameters are known, and our analysis clarifies the structural obstacles that distinguish this setting from the tabular case. Finally, through extensive experimentation across diverse non-stationary benchmarks, we show that DARLING consistently surpasses the state-of-the-art methods.

You are a robot and you live in a Markov decision process (MDP) with a finite or an infinite number of transitions from state-action to next states. You got brains and so you plan before you act. Luckily, your roboparents equipped you with a generative model to do some Monte-Carlo planning. The world is waiting for you and you have no time to waste. You want your planning to be efficient. Sample-efficient. Indeed, you want to exploit the possible structure of the MDP by exploring only a subset of states reachable by following near-optimal policies. You want guarantees on sample complexity that depend on a measure of the quantity of near-optimal states. You want something, that is an extension of Monte-Carlo sampling (for estimating an expectation) to problems that alternate maximization (over actions) and expectation (over next states). But you do not want to StOP with exponential running time, you want something simple to implement and computationally efficient. You want it all and you want it now. You want TrailBlazer.

We study reward poisoning attacks in reinforcement learning (RL), where an adversary manipulates rewards within constrained budgets to force the target RL agent to adopt a policy that aligns with the attacker's objectives. Prior works on reward poisoning mainly focused on sufficient conditions to design a successful attacker, while only a few studies discussed the infeasibility of targeted attacks. This paper provides the first precise necessity and sufficiency characterization of the attackability of a linear MDP under reward poisoning attacks. Our characterization draws a bright line between the vulnerable RL instances, and the intrinsically robust ones which cannot be attacked without large costs even running vanilla non-robust RL algorithms. Our theory extends beyond linear MDPs -- by approximating deep RL environments as linear MDPs, we show that our theoretical framework effectively distinguishes the attackability and efficiently attacks the vulnerable ones, demonstrating both the theoretical and practical significance of our characterization.

We study reinforcement learning (RL) with linear function approximation in Markov Decision Processes (MDPs) satisfying \emph{linear Bellman completeness} -- a fundamental setting where the Bellman backup of any linear value function remains linear. While statistically tractable, prior computationally efficient algorithms are either limited to small action spaces or require strong oracle assumptions over the feature space. We provide a computationally efficient algorithm for linear Bellman complete MDPs with \emph{deterministic transitions}, stochastic initial states, and stochastic rewards. For finite action spaces, our algorithm is end-to-end efficient; for large or infinite action spaces, we require only a standard argmax oracle over actions. Our algorithm learns an $\varepsilon$-optimal policy with sample and computational complexity polynomial in the horizon, feature dimension, and $1/\varepsilon$.

Tail-end risk measures such as static conditional value-at-risk (CVaR) are used in safety-critical applications to prevent rare, yet catastrophic events. Unlike risk-neutral objectives, the static CVaR of the return depends on entire trajectories without admitting a recursive Bellman decomposition in the underlying Markov decision process. A classical resolution relies on state augmentation with a continuous variable. However, unless restricted to a specialized class of admissible value functions, this formulation induces sparse rewards and degenerate fixed points. In this work, we propose a novel formulation of the static CVaR objective based on augmentation. Our alternative approach leads to a Bellman operator with: (1) dense per-step rewards; (2) contracting properties on the full space of bounded value functions. Building on this theoretical foundation, we develop risk-averse value iteration and model-free Q-learning algorithms that rely on discretized augmented states. We further provide convergence guarantees and approximation error bounds due to discretization. Empirical results demonstrate that our algorithms successfully learn CVaR-sensitive policies and achieve effective performance-safety trade-offs.

This work studies online episodic tabular Markov decision processes (MDPs) with known transitions and develops best-of-both-worlds algorithms that achieve refined data-dependent regret bounds in the adversarial regime and variance-dependent regret bounds in the stochastic regime. We quantify MDP complexity using a first-order quantity and several new data-dependent measures for the adversarial regime, including a second-order quantity and a path-length measure, as well as variance-based measures for the stochastic regime. To adapt to these measures, we develop algorithms based on global optimization and policy optimization, both built on optimistic follow-the-regularized-leader with log-barrier regularization. For global optimization, our algorithms achieve first-order, second-order, and path-length regret bounds in the adversarial regime, and in the stochastic regime, they achieve a variance-aware gap-independent bound and a variance-aware gap-dependent bound that is polylogarithmic in the number of episodes. For policy optimization, our algorithms achieve the same data- and variance-dependent adaptivity, up to a factor of the episode horizon, by exploiting a new optimistic $Q$-function estimator. Finally, we establish regret lower bounds in terms of data-dependent complexity measures for the adversarial regime and a variance measure for the stochastic regime, implying that the regret upper bounds achieved by the global-optimization approach are nearly optimal.

We are interested in enabling autonomous agents to learn and reason about systems with hidden states, such as locking mechanisms. We cast this problem as learning the parameters of a discrete Partially Observable Markov Decision Process (POMDP). The agent begins with knowledge of the POMDP's actions and observation spaces, but not its state space, transitions, or observation models. These properties must be constructed from a sequence of actions and observations. Spectral approaches to learning models of partially observable domains, such as Predictive State Representations (PSRs), learn representations of state that are sufficient to predict future outcomes. PSR models, however, do not have explicit transition and observation system models that can be used with different reward functions to solve different planning problems. Under a mild set of rankness assumptions on the products of transition and observation matrices, we show how PSRs learn POMDP matrices up to a similarity transform, and this transform may be estimated via tensor decomposition methods. Our method learns observation matrices and transition matrices up to a partition of states, where the states in a single partition have the same observation distributions corresponding to actions whose transition matrices are full-rank. Our numerical experiments suggest that explicit observation and transition likelihoods can be leveraged to generate new plans for different goals and reward functions after the model has been learned. We also show that learning a POMDP beyond a partition of states is impossible from sequential data by constructing two POMDPs that agree on all observation distributions but differ in their transition dynamics.

We present a novel probabilistic approach for optimal experimental path design. In this approach a discrete path optimization problem is defined on a static navigation mesh, and trajectories are modeled as random variables governed by a parametric Markov policy. The discrete path optimization problem is then replaced with an equivalent stochastic optimization problem over the policy parameters, resulting in an optimal probability model that samples estimates of the optimal discrete path. This approach enables exploration of the utility function's distribution tail and treats the utility function of the design as a black box, making it applicable to linear and nonlinear inverse problems and beyond experimental design. Numerical verification and analysis are carried out by using a parameter identification problem widely used in model-based optimal experimental design, namely a two-dimensional time-dependent advection diffusion problem in which the initial condition is the inference target. Experiments use both coarse and fine navigation meshes, with either a single moving sensor or a group of seven coordinated sensors, and the proposed approach is evaluated under D-, A-, and E-optimality criteria.

We study \emph{online episodic Constrained Markov Decision Processes} (CMDPs) under both stochastic and adversarial constraints. We provide a novel algorithm whose guarantees greatly improve those of the state-of-the-art best-of-both-worlds algorithm introduced by Stradi et al. (2025). In the stochastic regime, \emph{i.e.}, when the constraints are sampled from fixed but unknown distributions, our method achieves $\widetilde{\mathcal{O}}(\sqrt{T})$ regret and constraint violation without relying on Slater's condition, thereby handling settings where no strictly feasible solution exists. Moreover, we provide guarantees on the stronger notion of \emph{positive} constraint violation, which does not allow to recover from large violation in the early episodes by playing strictly safe policies. In the adversarial regime, \emph{i.e.}, when the constraints may change arbitrarily between episodes, our algorithm ensures sublinear constraint violation without Slater's condition, and achieves sublinear $α$-regret with respect to the \emph{unconstrained} optimum, where $α$ is a suitably defined multiplicative approximation factor. We further validate our results through synthetic experiments, showing the practical effectiveness of our algorithm.

Penetration testing, the simulation of cyberattacks to identify security vulnerabilities, presents a sequential decision-making problem well-suited for reinforcement learning (RL) automation. Like many applications of RL to real-world problems, partial observability presents a major challenge, as it invalidates the Markov property present in Markov Decision Processes (MDPs). Partially Observable MDPs require history aggregation or belief state estimation to learn successful policies. We investigate stochastic, partially observable penetration testing scenarios over host networks of varying size, aiming to better reflect real-world complexity through more challenging and representative benchmarks. This approach leads to the development of more robust and transferable policies, which are crucial for ensuring reliable performance across diverse and unpredictable real-world environments. Using vanilla Proximal Policy Optimization (PPO) as a baseline, we compare a selection of PPO-based variants designed to mitigate partial observability, including frame-stacking, augmenting observations with historical information, and employing LSTM or TrXL architectures. We conduct a systematic empirical analysis of these algorithms across different host network sizes. We find that this task greatly benefits from history aggregation. Converging up to four times faster than other approaches. Manual inspection of the learned policies by the algorithms reveals clear distinctions and provides insights that go beyond quantitative results.

We propose and study distributionally robust Markov games (DR-MGs) with the average-reward criterion as a crucial framework for multi-agent decision-making under model mismatches and over extended horizons. Under a standard irreducible assumption, we first derive a correspondence between the optimal policies and the solutions of the robust Bellman equation, based on which we further show the existence of a stationary Nash Equilibrium (NE) of the game. We further study DR-MGs under a more general weakly communicating setting. We construct a set-valued map based on the constant-gain optimal robust Bellman operator and show that its value is a subset of the best-response policies. We further prove that this map admits a fixed point, which implies the existence of NE. We then design two algorithms, Robust Nash-Iteration and robust TD Descent, with provably convergent guarantees. Finally, we show that the NE under average-reward can be approximated by the ones for the discounted DR-MGs as the discount factor approaches one. Our studies provide a comprehensive theoretical and algorithmic foundation for decision-making in complex, uncertain, and long-running multi-player environments.

This paper presents a state representation framework for Markov decision processes (MDPs) that can be learned solely from state trajectories, requiring neither reward signals nor the actions executed by the agent. We propose learning the minimum action distance (MAD), defined as the minimum number of actions required to transition between states, as a fundamental metric that captures the underlying structure of an environment. MAD naturally enables critical downstream tasks such as goal-conditioned reinforcement learning and reward shaping by providing a dense, geometrically meaningful measure of progress. Our self-supervised learning approach constructs an embedding space where the distances between embedded state pairs correspond to their MAD, accommodating both symmetric and asymmetric approximations. We evaluate the framework on a comprehensive suite of environments with known MAD values, encompassing both deterministic and stochastic dynamics, as well as discrete and continuous state spaces, and environments with noisy observations. Empirical results demonstrate that the proposed approach not only efficiently learns accurate MAD representations across these diverse settings but also significantly outperforms existing state representation methods in terms of representation quality.

A universal controller for any robot morphology would greatly improve computational and data efficiency. Steps have been made towards such multi-robot control by utilizing contextual information about the properties of individual robots and exploiting their modular structure in the architecture of deep reinforcement learning agents. When the robots have highly dissimilar morphologies, however, this becomes a challenging problem, especially when the agent must generalize to new, unseen robots. In this paper, we posit that contextual features are often only partially available, but that they can be recovered through modular interactions. This can allow for better multi-robot control and generalization to contexts that are not seen during training. To this extent, we implement a transformer-based architecture with shared modular recurrence and evaluate its (generalization) performance on a large set of MuJoCo robots. The results show a substantial improvement in zero-shot generalization performance on robots with unseen dynamics, kinematics, and topologies, in four different environments.

Most existing safe reinforcement learning (RL) benchmarks focus on robotics and control tasks, offering limited relevance to high-stakes domains that involve structured constraints, mixed-integer decisions, and industrial complexity. This gap hinders the advancement and deployment of safe RL in critical areas such as energy systems, manufacturing, and supply chains. To address this limitation, we present SafeOR-Gym, a benchmark suite of nine operations research (OR) environments tailored for safe RL under complex constraints. Each environment captures a realistic planning, scheduling, or control problems characterized by cost-based constraint violations, planning horizons, and hybrid discrete-continuous action spaces. The suite integrates seamlessly with the Constrained Markov Decision Process (CMDP) interface provided by OmniSafe. We evaluate several state-of-the-art safe RL algorithms across these environments, revealing a wide range of performance: while some tasks are tractable, others expose fundamental limitations in current approaches. SafeORGym provides a challenging and practical testbed that aims to catalyze future research in safe RL for real-world decision-making problems.

Learning the optimal policy for Markov decision process problems (MDPs) from samples is a fundamental problem in online and data-driven decision-making. Function approximations are usually deployed to handle large or infinite state-action space. In our work, we consider the MDP problems with function approximation and we develop a new algorithm to solve it efficiently. Our algorithm is based on a linear programming (LP) reformulation and repeatedly resolves the identified reduced linear system as new transition samples arrive. After the optimal basis is identified, we show that, after $N$ resolving rounds, the expected averaged iterate achieves an instance-dependent $\widetilde O(C_{\mathrm{inst}}/N)$ objective shortfall and signed constraint residual. We separately account for the historical samples used for basis identification and the $d_2$ transition queries used in each resolving round, which yields the corresponding total transition-query complexity. We further complement our result with a \textit{robust} $O(1/\sqrt{N})$ bound that is independent of $Δ$. In comparison to the guarantees established in the previous literature, our instance dependent guarantee is tighter when the underlying instance is favorable, and the numerical experiments also reveal the wide applications and efficient empirical performances of our algorithms.

We introduce the Switching Non-Stationary Markov Decision Process (SNS-MDP) framework, in which the environment transitions among a finite set of MDPs governed by a latent Markov chain while the agent observes only the external state. We show that the long-term effect of this switching is equivalent to stationary dynamics parameterized by the stationary distribution of the hidden Markov chain. For fixed policies, we derive a closed-form expression for the SNS value function and prove that standard temporal-difference (TD) learning converges to it almost surely despite persistent non-stationarity. We further establish that policy iteration converges to the optimal policy of the equivalent averaged environment, and prove that tabular Q-learning converges almost surely to the optimal Q-function. The framework is validated on a wireless communication network with Markovian channel noise, demonstrating its practical efficacy for decision-making in rapidly time-varying systems.

In the zero-shot policy transfer (ZSPT) setting for contextual Markov decision processes (CMDP), agents train on a fixed, finite set of contexts and must generalize to new ones. Recent work has demonstrated that training on additional states, even if they are irrelevant for solving the current context, can improve generalization to unseen contexts. In this paper, we demonstrate that training on these states can indeed improve generalization, but can come at a cost of reducing the accuracy of the learned value function, which should hurt generalization. We hypothesize and demonstrate that increasing the agent's coverage by training on these additional states while also increasing the accuracy improves generalization even further. Inspired by this, we propose a simple approach Explore-Go that leverages existing pure exploration strategies in a new way: by introducing a pure exploration phase at the start of each training episode. Unlike previous approaches that apply exploration strategies for the purpose of improving generalization, our approach can be combined with both on- and off-policy algorithms. We demonstrate the effectiveness of Explore-Go when combined with several popular algorithms and show an increase in test-time performance across several generalization benchmarks, even partially observable ones. With this, we hope to provide practitioners with a simple modification that can significantly improve the generalization of their agents.

This paper develops a framework for learning in discounted infinite-horizon Markov decision processes (MDPs) with Borel state and action spaces, whose rewards and transitions depend on an unknown parameter.To analyze sampling-based adaptive learning algorithms in this setting, we introduce a canonical probability space that explicitly incorporates sampled parameters into the history of the process. As a performance criterion, we adopt the per-period suboptimality gap used in discounted-MDP regret analysis and specialize it to our parametrized Bayesian setting. Since this quantity captures the remaining loss in future performance from the current period onward, we refer to it as residual regret. We use the expected residual regret to connect discounted-MDP regret analysis with asymptotic discount optimality from adaptive control and the temporal-difference error perspective from reinforcement learning. We then focus on Thompson sampling (TS) in discounted infinite-horizon MDPs. Under assumptions that extend those used in prior work on finite state and action spaces to the Borel setting, we show that the expected residual regret for TS converges to zero exponentially fast. We further show that, under mild conditions ensuring the existence of the relevant limits, the ample-path residual regret converges to zero almost surely and TS achieves complete learning.

The sim-to-real gap, which represents the disparity between training and testing environments, poses a significant challenge in reinforcement learning (RL). A promising approach to addressing this challenge is distributionally robust RL, often framed as a robust Markov decision process (RMDP). In this framework, the objective is to find a robust policy that achieves good performance under the worst-case scenario among all environments within a pre-specified uncertainty set centered around the training environment. Unlike previous work, which relies on a generative model or a pre-collected offline dataset enjoying good coverage of the deployment environment, we tackle robust RL via interactive data collection, where the learner interacts with the training environment only and refines the policy through trial and error. In this robust RL paradigm, two main challenges emerge: managing distributional robustness while striking a balance between exploration and exploitation during data collection. Initially, we establish that sample-efficient learning without additional assumptions is unattainable owing to the curse of support shift; i.e., the potential disjointedness of the distributional supports between the training and testing environments. To circumvent such a hardness result, we introduce the vanishing minimal value assumption to RMDPs with a total-variation (TV) distance robust set, postulating that the minimal value of the optimal robust value function is zero. We prove that such an assumption effectively eliminates support shift pathologies for RMDPs with a TV distance robust set, and present an algorithm with near-optimal sample complexity. To demonstrate the breadth of our framework, we extend our algorithm and theory to new robust set formulations and robust Markov games. To illustrate the operational relevance, we apply our algorithm to data-driven robust inventory control.

Federated learning is a distributed machine learning technology, which realizes the balance between data privacy protection and data sharing computing. To protect data privacy, feder-ated learning learns shared models by locally executing distributed training on participating devices and aggregating local models into global models. There is a problem in federated learning, that is, the negative impact caused by the non-independent and identical distribu-tion of data across different user terminals. In order to alleviate this problem, this paper pro-poses a strengthened federation aggregation method based on adaptive OPTICS clustering. Specifically, this method perceives the clustering environment as a Markov decision process, and models the adjustment process of parameter search direction, so as to find the best clus-tering parameters to achieve the best federated aggregation method. The core contribution of this paper is to propose an adaptive OPTICS clustering algorithm for federated learning. The algorithm combines OPTICS clustering and adaptive learning technology, and can effective-ly deal with the problem of non-independent and identically distributed data across different user terminals. By perceiving the clustering environment as a Markov decision process, the goal is to find the best parameters of the OPTICS cluster without artificial assistance, so as to obtain the best federated aggregation method and achieve better performance. The reliability and practicability of this method have been verified on the experimental data, and its effec-tiveness and superiority have been proved.

Most learning algorithms with formal regret guarantees essentially rely on trying all possible behaviors, which is problematic when some errors cannot be recovered from. Instead, we allow the learning agent to ask for help from a mentor and to transfer knowledge between similar states. We show that this combination enables the agent to learn both safely and effectively. Under standard online learning assumptions, we provide an algorithm whose regret and number of mentor queries are both sublinear in the time horizon for Markov decision processes with irreversible dynamics and infinite state spaces. Our proof involves a sequence of three reductions, making our result more general than a single algorithm. Conceptually, our result may be the first formal proof that it is possible for an agent to obtain high reward while becoming self-sufficient in an unknown, unbounded, and high-stakes environment without resets.

We present an optimization-based framework for robust permissive synthesis for Interval Markov Decision Processes (IMDPs). While robust IMDP controller synthesis typically yields a single policy and most permissive-synthesis methods assume exact transition models, we synthesize multi-strategies that retain multiple actions while guaranteeing satisfaction of probabilistic reachability or expected-reward specifications under all admissible transition probabilities. We formulate the problem as a mixed-integer linear program (MILP) that maximizes the number of enabled state--action pairs subject to robust Bellman constraints. We develop two encodings: a direct vertex-enumeration formulation and a dualization-based formulation that avoids explicit enumeration of uncertainty-polytope vertices and has size linear in the number of successor transitions. Experiments on four benchmark domains show that both encodings achieve the same optimal permissiveness and scale to IMDPs with hundreds of thousands of states. Compared with standard robust single-policy synthesis, the resulting multi-strategies retain substantially more action choices.