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We study optimality for the safety-constrained Markov decision process which is the underlying framework for safe reinforcement learning. Specifically, we consider a constrained Markov decision process (with finite states and finite actions) where the goal of the decision maker is to reach a target set while avoiding an unsafe set(s) with certain probabilistic guarantees. Therefore the underlying Markov chain for any control policy will be multichain since by definition there exists a target set and an unsafe set. The decision maker also has to be optimal (with respect to a cost function) while navigating to the target set. This gives rise to a multi-objective optimization problem. We highlight the fact that Bellman's principle of optimality may not hold for constrained Markov decision problems with an underlying multichain structure (as shown by the counterexample due to Haviv. We resolve the counterexample by formulating the aforementioned multi-objective optimization problem as a zero-sum game and thereafter construct an asynchronous value iteration scheme for the Lagrangian (similar to Shapley's algorithm). Finally, we consider the reinforcement learning problem for the same and construct a modified $Q$-learning algorithm for learning the Lagrangian from data. We also provide a lower bound on the number of iterations required for learning the Lagrangian and corresponding error bounds.

Transformers have significantly impacted domains like natural language processing, computer vision, and robotics, where they improve performance compared to other neural networks. This survey explores how transformers are used in reinforcement learning (RL), where they are seen as a promising solution for addressing challenges such as unstable training, credit assignment, lack of interpretability, and partial observability. We begin by providing a brief domain overview of RL, followed by a discussion on the challenges of classical RL algorithms. Next, we delve into the properties of the transformer and its variants and discuss the characteristics that make them well-suited to address the challenges inherent in RL. We examine the application of transformers to various aspects of RL, including representation learning, transition and reward function modeling, and policy optimization. We also discuss recent research that aims to enhance the interpretability and efficiency of transformers in RL, using visualization techniques and efficient training strategies. Often, the transformer architecture must be tailored to the specific needs of a given application. We present a broad overview of how transformers have been adapted for several applications, including robotics, medicine, language modeling, cloud computing, and combinatorial optimization. We conclude by discussing the limitations of using transformers in RL and assess their potential for catalyzing future breakthroughs in this field.

Recent studies show that deep reinforcement learning (DRL) agents tend to overfit to the task on which they were trained and fail to adapt to minor environment changes. To expedite learning when transferring to unseen tasks, we propose a novel approach to representing the current task using reward machines (RM), state machine abstractions that induce subtasks based on the current task's rewards and dynamics. Our method provides agents with symbolic representations of optimal transitions from their current abstract state and rewards them for achieving these transitions. These representations are shared across tasks, allowing agents to exploit knowledge of previously encountered symbols and transitions, thus enhancing transfer. Our empirical evaluation shows that our representations improve sample efficiency and few-shot transfer in a variety of domains.

Catastrophic interference is common in many network-based learning systems, and many proposals exist for mitigating it. Before overcoming interference we must understand it better. In this work, we provide a definition and novel measure of interference for value-based reinforcement learning methods such as Fitted Q-Iteration and DQN. We systematically evaluate our measure of interference, showing that it correlates with instability in control performance, across a variety of network architectures. Our new interference measure allows us to ask novel scientific questions about commonly used deep learning architectures and study learning algorithms which mitigate interference. Lastly, we outline a class of algorithms which we call online-aware that are designed to mitigate interference, and show they do reduce interference according to our measure and that they improve stability and performance in several classic control environments.

While Reinforcement Learning (RL) achieves tremendous success in sequential decision-making problems of many domains, it still faces key challenges of data inefficiency and the lack of interpretability. Interestingly, many researchers have leveraged insights from the causality literature recently, bringing forth flourishing works to unify the merits of causality and address well the challenges from RL. As such, it is of great necessity and significance to collate these Causal Reinforcement Learning (CRL) works, offer a review of CRL methods, and investigate the potential functionality from causality toward RL. In particular, we divide existing CRL approaches into two categories according to whether their causality-based information is given in advance or not. We further analyze each category in terms of the formalization of different models, ranging from the Markov Decision Process (MDP), Partially Observed Markov Decision Process (POMDP), Multi-Arm Bandits (MAB), and Dynamic Treatment Regime (DTR). Moreover, we summarize the evaluation matrices and open sources while we discuss emerging applications, along with promising prospects for the future development of CRL.

Knowledge-enhanced neural machine reasoning has garnered significant attention as a cutting-edge yet challenging research area with numerous practical applications. Over the past few years, plenty of studies have leveraged various forms of external knowledge to augment the reasoning capabilities of deep models, tackling challenges such as effective knowledge integration, implicit knowledge mining, and problems of tractability and optimization. However, there is a dearth of a comprehensive technical review of the existing knowledge-enhanced reasoning techniques across the diverse range of application domains. This survey provides an in-depth examination of recent advancements in the field, introducing a novel taxonomy that categorizes existing knowledge-enhanced methods into two primary categories and four subcategories. We systematically discuss these methods and highlight their correlations, strengths, and limitations. Finally, we elucidate the current application domains and provide insight into promising prospects for future research.

Graph mining tasks arise from many different application domains, ranging from social networks, transportation, E-commerce, etc., which have been receiving great attention from the theoretical and algorithm design communities in recent years, and there has been some pioneering work using the hotly researched reinforcement learning (RL) techniques to address graph data mining tasks. However, these graph mining algorithms and RL models are dispersed in different research areas, which makes it hard to compare different algorithms with each other. In this survey, we provide a comprehensive overview of RL models and graph mining and generalize these algorithms to Graph Reinforcement Learning (GRL) as a unified formulation. We further discuss the applications of GRL methods across various domains and summarize the method description, open-source codes, and benchmark datasets of GRL methods. Finally, we propose possible important directions and challenges to be solved in the future. This is the latest work on a comprehensive survey of GRL literature, and this work provides a global view for researchers as well as a learning resource for researchers outside the domain. In addition, we create an online open-source for both interested researchers who want to enter this rapidly developing domain and experts who would like to compare GRL methods.

The rapid changes in the finance industry due to the increasing amount of data have revolutionized the techniques on data processing and data analysis and brought new theoretical and computational challenges. In contrast to classical stochastic control theory and other analytical approaches for solving financial decision-making problems that heavily reply on model assumptions, new developments from reinforcement learning (RL) are able to make full use of the large amount of financial data with fewer model assumptions and to improve decisions in complex financial environments. This survey paper aims to review the recent developments and use of RL approaches in finance. We give an introduction to Markov decision processes, which is the setting for many of the commonly used RL approaches. Various algorithms are then introduced with a focus on value and policy based methods that do not require any model assumptions. Connections are made with neural networks to extend the framework to encompass deep RL algorithms. Our survey concludes by discussing the application of these RL algorithms in a variety of decision-making problems in finance, including optimal execution, portfolio optimization, option pricing and hedging, market making, smart order routing, and robo-advising.

This paper surveys the field of transfer learning in the problem setting of Reinforcement Learning (RL). RL has been the key solution to sequential decision-making problems. Along with the fast advance of RL in various domains. including robotics and game-playing, transfer learning arises as an important technique to assist RL by leveraging and transferring external expertise to boost the learning process. In this survey, we review the central issues of transfer learning in the RL domain, providing a systematic categorization of its state-of-the-art techniques. We analyze their goals, methodologies, applications, and the RL frameworks under which these transfer learning techniques would be approachable. We discuss the relationship between transfer learning and other relevant topics from an RL perspective and also explore the potential challenges as well as future development directions for transfer learning in RL.