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.

Estimating the structure of a Bayesian network, in the form of a directed acyclic graph (DAG), from observational data is a statistically and computationally hard problem with essential applications in areas such as causal discovery. Bayesian approaches are a promising direction for solving this task, as they allow for uncertainty quantification and deal with well-known identifiability issues. From a probabilistic inference perspective, the main challenges are (i) representing distributions over graphs that satisfy the DAG constraint and (ii) estimating a posterior over the underlying combinatorial space. We propose an approach that addresses these challenges by formulating a joint distribution on an augmented space of DAGs and permutations. We carry out posterior estimation via variational inference, where we exploit continuous relaxations of discrete distributions. We show that our approach can outperform competitive Bayesian and non-Bayesian benchmarks on a range of synthetic and real datasets.

Safe exploration is a challenging and important problem in model-free reinforcement learning (RL). Often the safety cost is sparse and unknown, which unavoidably leads to constraint violations -- a phenomenon ideally to be avoided in safety-critical applications. We tackle this problem by augmenting the state-space with a safety state, which is nonnegative if and only if the constraint is satisfied. The value of this state also serves as a distance toward constraint violation, while its initial value indicates the available safety budget. This idea allows us to derive policies for scheduling the safety budget during training. We call our approach Simmer (Safe policy IMproveMEnt for RL) to reflect the careful nature of these schedules. We apply this idea to two safe RL problems: RL with constraints imposed on an average cost, and RL with constraints imposed on a cost with probability one. Our experiments suggest that "simmering, a safe algorithm can improve safety during training for both settings. We further show that Simmer can stabilize training and improve the performance of safe RL with average constraints.

Satisfying safety constraints almost surely (or with probability one) can be critical for deployment of Reinforcement Learning (RL) in real-life applications. For example, plane landing and take-off should ideally occur with probability one. We address the problem by introducing Safety Augmented (Saute) Markov Decision Processes (MDPs), where the safety constraints are eliminated by augmenting them into the state-space and reshaping the objective. We show that Saute MDP satisfies the Bellman equation and moves us closer to solving Safe RL with constraints satisfied almost surely. We argue that Saute MDP allows to view Safe RL problem from a different perspective enabling new features. For instance, our approach has a plug-and-play nature, i.e., any RL algorithm can be "sauteed". Additionally, state augmentation allows for policy generalization across safety constraints. We finally show that Saute RL algorithms can outperform their state-of-the-art counterparts when constraint satisfaction is of high importance.

Portfolio management (PM) is a fundamental financial planning task that aims to achieve investment goals such as maximal profits or minimal risks. Its decision process involves continuous derivation of valuable information from various data sources and sequential decision optimization, which is a prospective research direction for reinforcement learning (RL). In this paper, we propose SARL, a novel State-Augmented RL framework for PM. Our framework aims to address two unique challenges in financial PM: (1) data heterogeneity -- the collected information for each asset is usually diverse, noisy and imbalanced (e.g., news articles); and (2) environment uncertainty -- the financial market is versatile and non-stationary. To incorporate heterogeneous data and enhance robustness against environment uncertainty, our SARL augments the asset information with their price movement prediction as additional states, where the prediction can be solely based on financial data (e.g., asset prices) or derived from alternative sources such as news. Experiments on two real-world datasets, (i) Bitcoin market and (ii) HighTech stock market with 7-year Reuters news articles, validate the effectiveness of SARL over existing PM approaches, both in terms of accumulated profits and risk-adjusted profits. Moreover, extensive simulations are conducted to demonstrate the importance of our proposed state augmentation, providing new insights and boosting performance significantly over standard RL-based PM method and other baselines.

In order to satisfy safety conditions, a reinforcement learned (RL) agent maybe constrained from acting freely, e.g., to prevent trajectories that might cause unwanted behavior or physical damage in a robot. We propose a general framework for augmenting a Markov decision process (MDP) with constraints that are described in formal languages over sequences of MDP states and agent actions. Constraint enforcement is implemented by filtering the allowed action set or by applying potential-based reward shaping to implement hard and soft constraint enforcement, respectively. We instantiate this framework using deterministic finite automata to encode constraints and propose methods of augmenting MDP observations with the state of the constraint automaton for learning. We empirically evaluate these methods with a variety of constraints by training Deep Q-Networks in Atari games as well as Proximal Policy Optimization in MuJoCo environments. We experimentally find that our approaches are effective in significantly reducing or eliminating constraint violations with either minimal negative or, depending on the constraint, a clear positive impact on final performance.