We consider a multi-agent Markov strategic interaction over an infinite horizon where agents can be of multiple types. We model the strategic interaction as a mean-field game in the asymptotic limit when the number of agents of each type becomes infinite. Each agent has a private state; the state evolves depending on the distribution of the state of the agents of different types and the action of the agent. Each agent wants to maximize the discounted sum of rewards over the infinite horizon which depends on the state of the agent and the distribution of the state of the leaders and followers. We seek to characterize and compute a stationary multi-type Mean field equilibrium (MMFE) in the above game. We characterize the conditions under which a stationary MMFE exists. Finally, we propose Reinforcement learning (RL) based algorithm using policy gradient approach to find the stationary MMFE when the agents are unaware of the dynamics. We, numerically, evaluate how such kind of interaction can model the cyber attacks among defenders and adversaries, and show how RL based algorithm can converge to an equilibrium.
This paper studies the adaptive optimal stationary control of continuous-time linear stochastic systems with both additive and multiplicative noises, using reinforcement learning techniques. Based on policy iteration, a novel off-policy reinforcement learning algorithm, named optimistic least-squares-based policy iteration, is proposed which is able to find iteratively near-optimal policies of the adaptive optimal stationary control problem directly from input/state data without explicitly identifying any system matrices, starting from an initial admissible control policy. The solutions given …
McCombs School of Business（麦库姆斯商学院）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）
Offline reinforcement learning (RL) extends the paradigm of classical RL algorithms to purely learning from static datasets, without interacting with the underlying environment during the learning process. A key challenge of offline RL is the instability of policy training, caused by the mismatch between the distribution of the offline data and the undiscounted stationary state-action distribution of the learned policy. To avoid the detrimental impact of distribution mismatch, we regularize the undiscounted stationary distribution of the current policy towards the offline data during the polic…
Indian Institute of Science（印度科学学院）；Indian Institute of Technology, Dharwad（印度理工学院达尔瓦德分校）
Reinforcement learning (RL) methods learn optimal decisions in the presence of a stationary environment. However, the stationary assumption on the environment is very restrictive. In many real world problems like traffic signal control, robotic applications, one often encounters situations with non-stationary environments and in these scenarios, RL methods yield sub-optimal decisions. In this paper, we thus consider the problem of developing RL methods that obtain optimal decisions in a non-stationary environment. The goal of this problem is to maximize the long-term discounted reward achieved…
Safety is a critical concern when deploying reinforcement learning agents for realistic tasks. Recently, safe reinforcement learning algorithms have been developed to optimize the agent's performance while avoiding violations of safety constraints. However, few studies have addressed the non-stationary disturbances in the environments, which may cause catastrophic outcomes. In this paper, we propose the context-aware safe reinforcement learning (CASRL) method, a meta-learning framework to realize safe adaptation in non-stationary environments. We use a probabilistic latent variable model to ac…
Nanjing University（南京大学）；East China Normal University（华东师范大学）
This paper addresses policy learning in non-stationary environments and games with continuous actions. Rather than the classical reward maximization mechanism, inspired by the ideas of follow-the-regularized-leader (FTRL) and mirror descent (MD) update, we propose a no-regret style reinforcement learning algorithm PORL for continuous action tasks. We prove that PORL has a last-iterate convergence guarantee, which is important for adversarial and cooperative games. Empirical studies show that, in stationary environments such as MuJoCo locomotion controlling tasks, PORL performs equally well as,…
Coordinated Science Laboratory, University of Illinois at Urbana–Champaign（伊利诺伊大学厄巴纳-香槟分校协同科学实验室）
In this paper, we study large population multi-agent reinforcement learning (RL) in the context of discrete-time linear-quadratic mean-field games (LQ-MFGs). Our setting differs from most existing work on RL for MFGs, in that we consider a non-stationary MFG over an infinite horizon. We propose an actor-critic algorithm to iteratively compute the mean-field equilibrium (MFE) of the LQ-MFG. There are two primary challenges: i) the non-stationarity of the MFG induces a linear-quadratic tracking problem, which requires solving a backwards-in-time (non-causal) equation that cannot be solved by sta…
Solving Continuous Mean Field Games: Deep Reinforcement Learning for Non-Stationary Dynamics
University of Cambridge（剑桥大学）；KTH Royal Institute of Technology（皇家理工学院）；University of California, Los Angeles（加州大学洛杉矶分校）；NYU Center for Data Science（纽约大学数据科学中心）；NYU Shanghai（纽约大学上海分校）
University of Bologna（博洛尼亚大学）；University of Michigan（密歇根大学）；Purdue University（普渡大学）
High-dimensional always-changing environments constitute a hard challenge for current reinforcement learning techniques. Artificial agents, nowadays, are often trained off-line in very static and controlled conditions in simulation such that training observations can be thought as sampled i.i.d. from the entire observations space. However, in real world settings, the environment is often non-stationary and subject to unpredictable, frequent changes. In this paper we propose and openly release CRLMaze, a new benchmark for learning continually through reinforcement in a complex 3D non-stationary…
We propose a black-box reduction that turns a certain reinforcement learning algorithm with optimal regret in a (near-)stationary environment into another algorithm with optimal dynamic regret in a non-stationary environment, importantly without any prior knowledge on the degree of non-stationarity. By plugging different algorithms into our black-box, we provide a list of examples showing that our approach not only recovers recent results for (contextual) multi-armed bandits achieved by very specialized algorithms, but also significantly improves the state of the art for (generalized) linear b…
We consider un-discounted reinforcement learning (RL) in Markov decision processes (MDPs) under drifting non-stationarity, i.e., both the reward and state transition distributions are allowed to evolve over time, as long as their respective total variations, quantified by suitable metrics, do not exceed certain variation budgets. We first develop the Sliding Window Upper-Confidence bound for Reinforcement Learning with Confidence Widening (SWUCRL2-CW) algorithm, and establish its dynamic regret bound when the variation budgets are known. In addition, we propose the Bandit-over-Reinforcement Le…
We consider the offline constrained reinforcement learning (RL) problem, in which the agent aims to compute a policy that maximizes expected return while satisfying given cost constraints, learning only from a pre-collected dataset. This problem setting is appealing in many real-world scenarios, where direct interaction with the environment is costly or risky, and where the resulting policy should comply with safety constraints. However, it is challenging to compute a policy that guarantees satisfying the cost constraints in the offline RL setting, since the off-policy evaluation inherently ha…
TIMRL: A Novel Meta-Reinforcement Learning Framework for Non-Stationary and Multi-Task Environments
School of Marine Science and Technology, Northwestern Polytechnical University（西北工业大学海洋科学与技术学院）；School of Astronautics, Northwestern Polytechnical University（西北工业大学航天学院）
Inria Lille（里尔法国国家信息与自动化研究所）；Université de Lille（里尔大学）；OvGU（马格德堡大学）；Facebook AI Research（脸书人工智能研究院）；CNRS（法国国家科学研究中心）；DeepMind Paris（深度思维巴黎）
In this work, we propose KeRNS: an algorithm for episodic reinforcement learning in non-stationary Markov Decision Processes (MDPs) whose state-action set is endowed with a metric. Using a non-parametric model of the MDP built with time-dependent kernels, we prove a regret bound that scales with the covering dimension of the state-action space and the total variation of the MDP with time, which quantifies its level of non-stationarity. Our method generalizes previous approaches based on sliding windows and exponential discounting used to handle changing environments. We further propose a pract…
We are interested in learning models of non-stationary environments, which can be framed as a multi-task learning problem. Model-free reinforcement learning algorithms can achieve good asymptotic performance in multi-task learning at a cost of extensive sampling, due to their approach, which requires learning from scratch. While model-based approaches are among the most data efficient learning algorithms, they still struggle with complex tasks and model uncertainties. Meta-reinforcement learning addresses the efficiency and generalization challenges on multi task learning by quickly leveraging…
In this paper, we establish a subgame perfect equilibrium reinforcement learning (SPERL) framework for time-inconsistent (TIC) problems. In the context of RL, TIC problems are known to face two main challenges: the non-existence of natural recursive relationships between value functions at different time points and the violation of Bellman's principle of optimality that raises questions on the applicability of standard policy iteration algorithms for unprovable policy improvement theorems. We adapt an extended dynamic programming theory and propose a new class of algorithms, called backward po…
Tsinghua University（清华大学）；University of Washington（华盛顿大学）
This paper gives the first polynomial-time algorithm for tabular Markov Decision Processes (MDP) that enjoys a regret bound \emph{independent on the planning horizon}. Specifically, we consider tabular MDP with $S$ states, $A$ actions, a planning horizon $H$, total reward bounded by $1$, and the agent plays for $K$ episodes. We design an algorithm that achieves an $O\left(\mathrm{poly}(S,A,\log K)\sqrt{K}\right)$ regret in contrast to existing bounds which either has an additional $\mathrm{polylog}(H)$ dependency~\citep{zhang2020reinforcement} or has an exponential dependency on $S$~\citep{li2…
Tracking Drift: Variation-Aware Entropy Scheduling for Non-Stationary Reinforcement Learning
School of Future Technology, Southeast University, Nanjing, China（东南大学未来技术学院，南京，中国）；School of Automation, Southeast University, Nanjing, China（东南大学自动化学院，南京，中国）
University of California, Berkeley（加州大学伯克利分校）；Virginia Tech（弗吉尼亚理工大学）
We study risk-sensitive reinforcement learning (RL) based on an entropic risk measure in episodic non-stationary Markov decision processes (MDPs). Both the reward functions and the state transition kernels are unknown and allowed to vary arbitrarily over time with a budget on their cumulative variations. When this variation budget is known a prior, we propose two restart-based algorithms, namely Restart-RSMB and Restart-RSQ, and establish their dynamic regrets. Based on these results, we further present a meta-algorithm that does not require any prior knowledge of the variation budget and can …
City University of Hong Kong（香港城市大学）；Carnegie Mellon University（卡内基梅隆大学）；Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）；University of Amsterdam（阿姆斯特丹大学）；MIT-IBM Watson AI Lab（麻省理工学院-IBM沃森人工智能实验室）
Dealing with non-stationarity in environments (e.g., in the transition dynamics) and objectives (e.g., in the reward functions) is a challenging problem that is crucial in real-world applications of reinforcement learning (RL). While most current approaches model the changes as a single shared embedding vector, we leverage insights from the recent causality literature to model non-stationarity in terms of individual latent change factors, and causal graphs across different environments. In particular, we propose Factored Adaptation for Non-Stationary RL (FANS-RL), a factored adaption approach …
The Chinese University of Hong Kong (Shenzhen)（香港中文大学（深圳））
In recent years, many practitioners in quantitative finance have attempted to use Deep Reinforcement Learning (DRL) to build better quantitative trading (QT) strategies. Nevertheless, many existing studies fail to address several serious challenges, such as the non-stationary financial environment and the bias and variance trade-off when applying DRL in the real financial market. In this work, we proposed Safe-FinRL, a novel DRL-based high-freq stock trading strategy enhanced by the near-stationary financial environment and low bias and variance estimation. Our main contributions are twofold: …
We consider primal-dual-based reinforcement learning (RL) in episodic constrained Markov decision processes (CMDPs) with non-stationary objectives and constraints, which plays a central role in ensuring the safety of RL in time-varying environments. In this problem, the reward/utility functions and the state transition functions are both allowed to vary arbitrarily over time as long as their cumulative variations do not exceed certain known variation budgets. Designing safe RL algorithms in time-varying environments is particularly challenging because of the need to integrate the constraint vi…
We consider model-based multi-agent reinforcement learning, where the environment transition model is unknown and can only be learned via expensive interactions with the environment. We propose H-MARL (Hallucinated Multi-Agent Reinforcement Learning), a novel sample-efficient algorithm that can efficiently balance exploration, i.e., learning about the environment, and exploitation, i.e., achieve good equilibrium performance in the underlying general-sum Markov game. H-MARL builds high-probability confidence intervals around the unknown transition model and sequentially updates them based on ne…
Université de Toulouse（图卢兹大学）；ONERA - The French Aerospace Lab（法国航空航天实验室（ONERA））；ISAE-SUPAERO（法国高等航空航天学院）
This work tackles the problem of robust zero-shot planning in non-stationary stochastic environments. We study Markov Decision Processes (MDPs) evolving over time and consider Model-Based Reinforcement Learning algorithms in this setting. We make two hypotheses: 1) the environment evolves continuously with a bounded evolution rate; 2) a current model is known at each decision epoch but not its evolution. Our contribution can be presented in four points. 1) we define a specific class of MDPs that we call Non-Stationary MDPs (NSMDPs). We introduce the notion of regular evolution by making an hyp…
National University of Singapore（新加坡国立大学）；Massachusetts Institute of Technology（麻省理工学院）
We consider un-discounted reinforcement learning (RL) in Markov decision processes (MDPs) under temporal drifts, ie, both the reward and state transition distributions are allowed to evolve over time, as long as their respective total variations, quantified by suitable metrics, do not exceed certain variation budgets. This setting captures the endogeneity, exogeneity, uncertainty, and partial feedback in sequential decision-making scenarios, and finds applications in vehicle remarketing and real-time bidding. We first develop the Sliding Window Upper-Confidence bound for Reinforcement Learning…
MIT-LIDS（麻省理工学院信息与决策系统实验室）；MIT-IBM Watson AI Lab（麻省理工学院-IBM沃森人工智能实验室）；IBM-Research（IBM研究院）
A fundamental challenge in multiagent reinforcement learning is to learn beneficial behaviors in a shared environment with other simultaneously learning agents. In particular, each agent perceives the environment as effectively non-stationary due to the changing policies of other agents. Moreover, each agent is itself constantly learning, leading to natural non-stationarity in the distribution of experiences encountered. In this paper, we propose a novel meta-multiagent policy gradient theorem that directly accounts for the non-stationary policy dynamics inherent to multiagent learning setting…
We study learning in periodic Markov Decision Process(MDP), a special type of non-stationary MDP where both the state transition probabilities and reward functions vary periodically, under the average reward maximization setting. We formulate the problem as a stationary MDP by augmenting the state space with the period index, and propose a periodic upper confidence bound reinforcement learning-2 (PUCRL2) algorithm. We show that the regret of PUCRL2 varies linearly with the period and as sub-linear with the horizon length. Numerical results demonstrate the efficacy of PUCRL2.
Federal University of Rio Grande do Sul（里约热内卢联邦大学南里奥格兰德分校）；University of Massachusetts（马萨诸塞大学）
Non-stationary environments are challenging for reinforcement learning algorithms. If the state transition and/or reward functions change based on latent factors, the agent is effectively tasked with optimizing a behavior that maximizes performance over a possibly infinite random sequence of Markov Decision Processes (MDPs), each of which drawn from some unknown distribution. We call each such MDP a context. Most related works make strong assumptions such as knowledge about the distribution over contexts, the existence of pre-training phases, or a priori knowledge about the number, sequence, o…
This paper studies two important signal processing aspects of equilibrium behavior in non-cooperative games arising in social networks, namely, reinforcement learning and detection of equilibrium play. The first part of the paper presents a reinforcement learning (adaptive filtering) algorithm that facilitates learning an equilibrium by resorting to diffusion cooperation strategies in a social network. Agents form homophilic social groups, within which they exchange past experiences over an undirected graph. It is shown that, if all agents follow the proposed algorithm, their global behavior i…
City University of Hong Kong（香港城市大学）；Sun Yat-sen University（中山大学）
We propose a reinforcement learning (RL) approach to compute the expression of quasi-stationary distribution. Based on the fixed-point formulation of quasi-stationary distribution, we minimize the KL-divergence of two Markovian path distributions induced by the candidate distribution and the true target distribution. To solve this challenging minimization problem by gradient descent, we apply the reinforcement learning technique by introducing the reward and value functions. We derive the corresponding policy gradient theorem and design an actor-critic algorithm to learn the optimal solution a…
Institut d’Investigació en Intelligència Artificial（人工智能研究所）；Universidade Metodista de São Paulo（圣保罗卫理公会大学）；Centro Universitário FEI（FEI大学中心）
Non-stationary domains, where unforeseen changes happen, present a challenge for agents to find an optimal policy for a sequential decision making problem. This work investigates a solution to this problem that combines Markov Decision Processes (MDP) and Reinforcement Learning (RL) with Answer Set Programming (ASP) in a method we call ASP(RL). In this method, Answer Set Programming is used to find the possible trajectories of an MDP, from where Reinforcement Learning is applied to learn the optimal policy of the problem. Results show that ASP(RL) is capable of efficiently finding the optimal …
