Many ideas in modern control and reinforcement learning treat decision-making as inference: start from a baseline distribution and update it when a signal arrives. We ask when this can be made literal rather than metaphorical. We study the special case where a KL-regularized soft update is exactly a Bayesian posterior inside a single fixed probabilistic model, so the update variable is a genuine channel through which information is transmitted. In this regime, behavioral change is driven only by evidence carried by that channel: the update must be explainable as an evidence reweighing of the baseline. This yields a sharp identification result: posterior updates determine the relative, context-dependent incentive signal that shifts behavior, but they do not uniquely determine absolute rewards, which remain ambiguous up to context-specific baselines. Requiring one reusable continuation value across different update directions adds a further coherence constraint linking the reward descriptions associated with different conditioning orders.

Poisson equations underpin average-reward reinforcement learning, but beyond ergodicity they can be ill-posed, meaning that solutions are non-unique and standard fixed point iterations can oscillate on reducible or periodic chains. We study finite-state Markov chains with $n$ states and transition matrix $P$. We show that all non-decaying modes are captured by a real peripheral invariant subspace $\mathcal{K}(P)$, and that the induced operator on the quotient space $\mathbb{R}^n/\mathcal{K}(P)$ is strictly contractive, yielding a unique quotient solution. Building on this viewpoint, we develop an end-to-end pipeline that learns the chain structure, estimates an anchor based gauge map, and runs projected stochastic approximation to estimate a gauge-fixed representative together with an associated peripheral residual. We prove $\widetilde{O}(T^{-1/2})$ convergence up to projection estimation error, enabling stable Poisson equation learning for multichain and periodic regimes with applications to performance evaluation of average-reward reinforcement learning beyond ergodicity.

A/B testing has become a gold standard for modern technological companies to conduct policy evaluation. Yet, its application to time series experiments, where policies are sequentially assigned over time, remains challenging. Existing designs suffer from two limitations: (i) they do not fully leverage the entire history for treatment allocation; (ii) they rely on strong assumptions to approximate the objective function (e.g., the mean squared error of the estimated treatment effect) for optimizing the design. We first establish an impossibility theorem showing that failure to condition on the full history leads to suboptimal designs, due to the dynamic dependencies in time series experiments. To address both limitations simultaneously, we next propose a transformer reinforcement learning (RL) approach which leverages transformers to condition allocation on the entire history and employs RL to directly optimize the MSE without relying on restrictive assumptions. Empirical evaluations on synthetic data, a publicly available dispatch simulator, and a real-world ridesharing dataset demonstrate that our proposal consistently outperforms existing designs.

Most existing offline RL methods presume the availability of action labels within the dataset, but in many practical scenarios, actions may be missing due to privacy, storage, or sensor limitations. We formalise the setting of action-free offline-to-online RL, where agents must learn from datasets consisting solely of $(s,r,s')$ tuples and later leverage this knowledge during online interaction. To address this challenge, we propose learning state policies that recommend desirable next-state transitions rather than actions. Our contributions are twofold. First, we introduce a simple yet novel state discretisation transformation and propose Offline State-Only DecQN (\algo), a value-based algorithm designed to pre-train state policies from action-free data. \algo{} integrates the transformation to scale efficiently to high-dimensional problems while avoiding instability and overfitting associated with continuous state prediction. Second, we propose a novel mechanism for guided online learning that leverages these pre-trained state policies to accelerate the learning of online agents. Together, these components establish a scalable and practical framework for leveraging action-free datasets to accelerate online RL. Empirical results across diverse benchmarks demonstrate that our approach improves convergence speed and asymptotic performance, while analyses reveal that discretisation and regularisation are critical to its effectiveness.

In the last decade, Reinforcement Learning (RL) has achieved remarkable success in the control and decision-making of complex dynamical systems. However, most RL algorithms rely on the Markov Decision Process assumption, which is violated in practical cyber-physical systems affected by sensing delays, actuation latencies, and communication constraints. Such time delays introduce memory effects that can significantly degrade performance and compromise stability, particularly in networked and multi-agent environments. This paper presents a comprehensive survey of RL methods designed to address time delays in control systems. We first formalize the main classes of delays and analyze their impact on the Markov property. We then systematically categorize existing approaches into five major families: state augmentation and history-based representations, recurrent policies with learned memory, predictor-based and model-aware methods, robust and domain-randomized training strategies, and safe RL frameworks with explicit constraint handling. For each family, we discuss underlying principles, practical advantages, and inherent limitations. A comparative analysis highlights key trade-offs among these approaches and provides practical guidelines for selecting suitable methods under different delay characteristics and safety requirements. Finally, we identify open challenges and promising research directions, including stability certification, large-delay learning, multi-agent communication co-design, and standardized benchmarking. This survey aims to serve as a unified reference for researchers and practitioners developing reliable RL-based controllers in delay-affected cyber-physical systems.

We often collect data from multiple sites (e.g., hospitals) that share common structure but also exhibit heterogeneity. This paper aims to learn robust sequential decision-making policies from such offline, multi-site datasets. To model cross-site uncertainty, we study distributionally robust MDPs with a group-linear structure: all sites share a common feature map, and both the transition kernels and expected reward functions are linear in these shared features. We introduce feature-wise (d-rectangular) uncertainty sets, which preserve tractable robust Bellman recursions while maintaining key cross-site structure. Building on this, we then develop an offline algorithm based on pessimistic value iteration that includes: (i) per-site ridge regression for Bellman targets, (ii) feature-wise worst-case (row-wise minimization) aggregation, and (iii) a data-dependent pessimism penalty computed from the diagonals of the inverse design matrices. We further propose a cluster-level extension that pools similar sites to improve sample efficiency, guided by prior knowledge of site similarity. Under a robust partial coverage assumption, we prove a suboptimality bound for the resulting policy. Overall, our framework addresses multi-site learning with heterogeneous data sources and provides a principled approach to robust planning without relying on strong state-action rectangularity assumptions.

Online reinforcement learning in non-episodic, finite-horizon MDPs remains underexplored and is challenged by the need to estimate returns to a fixed terminal time. Existing infinite-horizon methods, which often rely on discounted contraction, do not naturally account for this fixed-horizon structure. We introduce a modified Q-function: rather than targeting the full-horizon, we learn a K-step lookahead Q-function that truncates planning to the next K steps. To further improve sample efficiency, we introduce a thresholding mechanism: actions are selected only when their estimated K-step lookahead value exceeds a time-varying threshold. We provide an efficient tabular learning algorithm for this novel objective, proving it achieves fast finite-sample convergence: it achieves minimax optimal constant regret for $K=1$ and $\mathcal{O}(\max((K-1),C_{K-1})\sqrt{SAT\log(T)})$ regret for any $K \geq 2$. We numerically evaluate the performance of our algorithm under the objective of maximizing reward. Our implementation adaptively increases K over time, balancing lookahead depth against estimation variance. Empirical results demonstrate superior cumulative rewards over state-of-the-art tabular RL methods across synthetic MDPs and RL environments: JumpRiverswim, FrozenLake and AnyTrading.

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We introduce the Value-at-Risk Constrained Policy Optimization algorithm (VaR-CPO), a sample efficient and conservative method designed to optimize Value-at-Risk (VaR) constraints directly. Empirically, we demonstrate that VaR-CPO is capable of safe exploration, achieving zero constraint violations during training in feasible environments, a critical property that baseline methods fail to uphold. To overcome the inherent non-differentiability of the VaR constraint, we employ the one-sided Chebyshev inequality to obtain a tractable surrogate based on the first two moments of the cost return. Additionally, by extending the trust-region framework of the Constrained Policy Optimization (CPO) method, we provide rigorous worst-case bounds for both policy improvement and constraint violation during the training process.

Reinforcement learning (RL) is a powerful framework for learning to take actions to solve tasks. However, in many settings, an agent must winnow down the inconceivably large space of all possible tasks to the single task that it is currently being asked to solve. Can we instead constrain the space of tasks to those that are semantically meaningful? In this work, we introduce a framework for using weak supervision to automatically disentangle this semantically meaningful subspace of tasks from the enormous space of nonsensical chaff tasks. We show that this learned subspace enables efficient exploration and provides a representation that captures distance between states. On a variety of challenging, vision-based continuous control problems, our approach leads to substantial performance gains, particularly as the complexity of the environment grows.