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.

We study offline imitation learning (IL) when part of the decision-relevant state is observed only through noisy measurements and the distribution may change between training and deployment. Such settings induce spurious state-action correlations, so standard behavioral cloning (BC) -- whether conditioning on raw measurements or ignoring them -- can converge to systematically biased policies under distribution shift. We propose a general framework for IL under measurement error, inspired by explicitly modeling the causal relationships among the variables, yielding a target that retains a causal interpretation and is robust to distribution shift. Building on ideas from proximal causal inference, we introduce \texttt{CausIL}, which treats noisy state observations as proxy variables, and we provide identification conditions under which the target policy is recoverable from demonstrations without rewards or interactive expert queries. We develop estimators for both discrete and continuous state spaces; for continuous settings, we use an adversarial procedure over RKHS function classes to learn the required parameters. We evaluate \texttt{CausIL} on semi-simulated longitudinal data from the PhysioNet/Computing in Cardiology Challenge 2019 cohort and demonstrate improved robustness to distribution shift compared to BC baselines.

Understanding the stability and long-time behavior of generative models is a fundamental problem in modern machine learning. This paper provides quantitative bounds on the sampling error of score-based generative models by leveraging stability and forgetting properties of the Markov chain associated with the reverse-time dynamics. Under weak assumptions, we provide the two structural properties to ensure the propagation of initialization and discretization errors of the backward process: a Lyapunov drift condition and a Doeblin-type minorization condition. A practical consequence is quantitative stability of the sampling procedure, as the reverse diffusion dynamics induces a contraction mechanism along the sampling trajectory. Our results clarify the role of stochastic dynamics in score-based models and provide a principled framework for analyzing propagation of errors in such approaches.

We study online transfer reinforcement learning (RL) in episodic Markov decision processes, where experience from related source tasks is available during learning on a target task. A fundamental difficulty is that task similarity is typically defined in terms of rewards or transitions, whereas online RL algorithms operate on Bellman regression targets. As a result, naively reusing source Bellman updates introduces systematic bias and invalidates regret guarantees. We identify one-step Bellman alignment as the correct abstraction for transfer in online RL and propose re-weighted targeting (RWT), an operator-level correction that retargets continuation values and compensates for transition mismatch via a change of measure. RWT reduces task mismatch to a fixed one-step correction and enables statistically sound reuse of source data. This alignment yields a two-stage RWT $Q$-learning framework that separates variance reduction from bias correction. Under RKHS function approximation, we establish regret bounds that scale with the complexity of the task shift rather than the target MDP. Empirical results in both tabular and neural network settings demonstrate consistent improvements over single-task learning and naïve pooling, highlighting Bellman alignment as a model-agnostic transfer principle for online RL.

Advances in data collection are producing growing volumes of temporal count observations, making adapted modeling increasingly necessary. In this work, we introduce a generative framework for independent component analysis of temporal count data, combining regime-adaptive dynamics with Poisson log-normal emissions. The model identifies disentangled components with regime-dependent contributions, enabling representation learning and perturbations analysis. Notably, we establish the identifiability of the model, supporting principled interpretation. To learn the parameters, we propose an efficient amortized variational inference procedure. Experiments on simulated data evaluate recovery of the mixing function and latent sources across diverse settings, while an in vivo longitudinal gut microbiome study reveals microbial co-variation patterns and regime shifts consistent with clinical perturbations.

We present the convergence rates of synchronous and asynchronous Q-learning for average-reward Markov decision processes, where the absence of contraction poses a fundamental challenge. Existing non-asymptotic results overcome this challenge by either imposing strong assumptions to enforce seminorm contraction or relying on discounted or episodic Markov decision processes as successive approximations, which either require unknown parameters or result in suboptimal sample complexity. In this work, under a reachability assumption, we establish optimal $\widetilde{O}(\varepsilon^{-2})$ sample complexity guarantees (up to logarithmic factors) for a simple variant of synchronous and asynchronous Q-learning that samples from the lazified dynamics, where the system remains in the current state with some fixed probability. At the core of our analysis is the construction of an instance-dependent seminorm and showing that, after a lazy transformation of the Markov decision process, the Bellman operator becomes one-step contractive under this seminorm.

Transformers often appear to perform Bayesian reasoning in context, but verifying this rigorously has been impossible: natural data lack analytic posteriors, and large models conflate reasoning with memorization. We address this by constructing \emph{Bayesian wind tunnels} -- controlled environments where the true posterior is known in closed form and memorization is provably impossible. In these settings, small transformers reproduce Bayesian posteriors with $10^{-3}$-$10^{-4}$ bit accuracy, while capacity-matched MLPs fail by orders of magnitude, establishing a clear architectural separation. Across two tasks -- bijection elimination and Hidden Markov Model (HMM) state tracking -- we find that transformers implement Bayesian inference through a consistent geometric mechanism: residual streams serve as the belief substrate, feed-forward networks perform the posterior update, and attention provides content-addressable routing. Geometric diagnostics reveal orthogonal key bases, progressive query-key alignment, and a low-dimensional value manifold parameterized by posterior entropy. During training this manifold unfurls while attention patterns remain stable, a \emph{frame-precision dissociation} predicted by recent gradient analyses. Taken together, these results demonstrate that hierarchical attention realizes Bayesian inference by geometric design, explaining both the necessity of attention and the failure of flat architectures. Bayesian wind tunnels provide a foundation for mechanistically connecting small, verifiable systems to reasoning phenomena observed in large language models.

The unification of neural and symbolic approaches to artificial intelligence remains a central open challenge. In this work, we introduce a tensor network formalism, which captures sparsity principles originating in the different approaches in tensor decompositions. In particular, we describe a basis encoding scheme for functions and model neural decompositions as tensor decompositions. The proposed formalism can be applied to represent logical formulas and probability distributions as structured tensor decompositions. This unified treatment identifies tensor network contractions as a fundamental inference class and formulates efficiently scaling reasoning algorithms, originating from probability theory and propositional logic, as contraction message passing schemes. The framework enables the definition and training of hybrid logical and probabilistic models, which we call Hybrid Logic Network. The theoretical concepts are accompanied by the python library tnreason, which enables the implementation and practical use of the proposed architectures.