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 violation reduction, safe exploration, and adaptation to the non-stationarity. To this end, we identify two alternative conditions on the time-varying constraints under which we can guarantee the safety in the long run. We also propose the \underline{P}eriodically \underline{R}estarted \underline{O}ptimistic \underline{P}rimal-\underline{D}ual \underline{P}roximal \underline{P}olicy \underline{O}ptimization (PROPD-PPO) algorithm that can coordinate with both two conditions. Furthermore, a dynamic regret bound and a constraint violation bound are established for the proposed algorithm in both the linear kernel CMDP function approximation setting and the tabular CMDP setting under two alternative conditions. This paper provides the first provably efficient algorithm for non-stationary CMDPs with safe exploration.
University of Michigan, Ann Arbor（密歇根大学安娜堡分校）；The Ohio State University（俄亥俄州立大学）；Wayne State University（韦恩州立大学）
We study model-free reinforcement learning (RL) algorithms in episodic non-stationary constrained Markov Decision Processes (CMDPs), in which an agent aims to maximize the expected cumulative reward subject to a cumulative constraint on the expected utility (cost). In the non-stationary environment, reward, utility functions, and transition kernels can vary arbitrarily over time as long as the cumulative variations do not exceed certain variation budgets. We propose the first model-free, simulator-free RL algorithms with sublinear regret and zero constraint violation for non-stationary CMDPs i…
Primal-Dual Policy Optimization for Linear CMDPs with Adversarial Losses
Research Institute of Mathematics, Seoul National University（数学研究所，首尔国立大学）；Interdisciplinary Program in Artificial Intelligence, Seoul National University（人工智能跨学科项目，首尔国立大学）；Korea Institute for Advanced Study（韩国高级研究院）
Constrained Markov Decision Process (CMDP) is a natural framework for reinforcement learning tasks with safety constraints, where agents learn a policy that maximizes the long-term reward while satisfying the constraints on the long-term cost. A canonical approach for solving CMDPs is the primal-dual method which updates parameters in primal and dual spaces in turn. Existing methods for CMDPs only use on-policy data for dual updates, which results in sample inefficiency and slow convergence. In this paper, we propose a policy search method for CMDPs called Accelerated Primal-Dual Optimization …
Peking University（北京大学）；National University of Singapore（新加坡国立大学）；Beijing International Center for Mathematical Research（北京国际数学研究中心）
As an important framework for safe Reinforcement Learning, the Constrained Markov Decision Process (CMDP) has been extensively studied in the recent literature. However, despite the rich results under various on-policy learning settings, there still lacks some essential understanding of the offline CMDP problems, in terms of both the algorithm design and the information theoretic sample complexity lower bound. In this paper, we focus on solving the CMDP problems where only offline data are available. By adopting the concept of the single-policy concentrability coefficient $C^*$, we establish a…
A Policy Gradient Primal-Dual Algorithm for Constrained MDPs with Uniform PAC Guarantees
The University of Tokyo（东京大学）；OMRON SINIC X（欧姆龙SINIC X公司）；Mizuho–DL Financial Technology（瑞穗-DL金融科技公司）；Nara Institute of Science and Technology（奈良先端科学技术大学院大学）；RIKEN Center for Advanced Intelligence Project（理化学研究所革新智能综合研究中心）；Osaka University（大阪大学）；Kyoto University（京都大学）
Purdue University（普渡大学）；US Army Research Laboratory（美国陆军研究实验室）
Reinforcement learning is widely used in applications where one needs to perform sequential decisions while interacting with the environment. The problem becomes more challenging when the decision requirement includes satisfying some safety constraints. The problem is mathematically formulated as constrained Markov decision process (CMDP). In the literature, various algorithms are available to solve CMDP problems in a model-free manner to achieve $ε$-optimal cumulative reward with $ε$ feasible policies. An $ε$-feasible policy implies that it suffers from constraint violation. An important ques…
University of Michigan（密歇根大学）；University of Southern California（南加州大学）；Princeton University（普林斯顿大学）；Northwestern University（西北大学）
We consider online learning for episodic stochastically constrained Markov decision processes (CMDPs), which plays a central role in ensuring the safety of reinforcement learning. Here the loss function can vary arbitrarily across the episodes, and both the loss received and the budget consumption are revealed at the end of each episode. Previous works solve this problem under the restrictive assumption that the transition model of the Markov decision processes (MDPs) is known a priori and establish regret bounds that depend polynomially on the cardinalities of the state space $\mathcal{S}$ an…
Provably Efficient RL under Episode-Wise Safety in Constrained MDPs with Linear Function Approximation
The University of Tokyo（东京大学）；New Jersey Institute of Technology（新泽西理工学院）；OMRON SINIC X（欧姆龙SINIC X）；NexaScience；Kyoto University（京都大学）；Institute of Science Tokyo（东京科学大学）；DENSO IT Laboratory（电装IT实验室）
Near-Constant Strong Violation and Last-Iterate Convergence for Online CMDPs via Decaying Safety Margins
School of Informatics, University of Edinburgh, Edinburgh, United Kingdom（爱丁堡大学信息学院）；School of Mathematics, University of Edinburgh, Edinburgh, United Kingdom（爱丁堡大学数学学院）
Near-Optimal Primal-Dual Algorithm for Learning Linear Mixture CMDPs with Adversarial Rewards
Department of Industrial and Systems Engineering, KAIST（韩国科学技术院工业与系统工程系）；Department of Mathematical Sciences, Seoul National University（首尔大学数学科学系）；Research Institute of Mathematics, Seoul National University（首尔大学数学研究所）；Interdisciplinary Program in Artificial Intelligence, Seoul National University（首尔大学人工智能跨学科项目）；Korea Institute for Advanced Study（韩国高等研究院）
Finite-Time Complexity of Online Primal-Dual Natural Actor-Critic Algorithm for Constrained Markov Decision Processes
School of Electrical and Computer Engineering, Georgia Institute of Technology（佐治亚理工学院电气与计算机工程学院）；Bradley Department of Electrical and Computer Engineering, Virginia Tech（弗吉尼亚理工大学布拉德利电气与计算机工程学院）
Achieving Instance-dependent Sample Complexity for Constrained Markov Decision Process
Department of Industrial Engineering & Decision Analytics, Hong Kong University of Science and Technology（香港科技大学工业工程与决策分析系）；Institute for Computational and Mathematical Engineering, Stanford University（斯坦福大学计算与数学工程研究所）；Department of Management Science & Engineering, Stanford University（斯坦福大学管理科学与工程系）
Technion（以色列理工学院）；Facebook AI Research（Facebook人工智能研究院）
In many sequential decision-making problems, the goal is to optimize a utility function while satisfying a set of constraints on different utilities. This learning problem is formalized through Constrained Markov Decision Processes (CMDPs). In this paper, we investigate the exploration-exploitation dilemma in CMDPs. While learning in an unknown CMDP, an agent should trade-off exploration to discover new information about the MDP, and exploitation of the current knowledge to maximize the reward while satisfying the constraints. While the agent will eventually learn a good or optimal policy, we …
The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；JD Explore Academy（京东探索研究院）
We study the convergence of the actor-critic algorithm with nonlinear function approximation under a nonconvex-nonconcave primal-dual formulation. Stochastic gradient descent ascent is applied with an adaptive proximal term for robust learning rates. We show the first efficient convergence result with primal-dual actor-critic with a convergence rate of $\mathcal{O}\left(\sqrt{\frac{\ln \left(N d G^2 \right)}{N}}\right)$ under Markovian sampling, where $G$ is the element-wise maximum of the gradient, $N$ is the number of iterations, and $d$ is the dimension of the gradient. Our result is presen…
This paper presents the first model-free, simulator-free reinforcement learning algorithm for Constrained Markov Decision Processes (CMDPs) with sublinear regret and zero constraint violation. The algorithm is named Triple-Q because it includes three key components: a Q-function (also called action-value function) for the cumulative reward, a Q-function for the cumulative utility for the constraint, and a virtual-Queue that (over)-estimates the cumulative constraint violation. Under Triple-Q, at each step, an action is chosen based on the pseudo-Q-value that is a combination of the three "Q" v…
Georgia Institute of Technology（佐治亚理工学院）；The Ohio State University（俄亥俄州立大学）；University at Buffalo, The State University of New York（纽约州立大学布法罗分校）
The problem of constrained Markov decision process (CMDP) is investigated, where an agent aims to maximize the expected accumulated discounted reward subject to multiple constraints on its utilities/costs. A new primal-dual approach is proposed with a novel integration of three ingredients: entropy regularized policy optimizer, dual variable regularizer, and Nesterov's accelerated gradient descent dual optimizer, all of which are critical to achieve a faster convergence. The finite-time error bound of the proposed approach is characterized. Despite the challenge of the nonconcave objective sub…
Global Convergence of Average Reward Constrained MDPs with Neural Critic and General Policy Parameterization
Department of Computer Science University of Maryland College Park（计算机科学系大学马里兰大学学院公园）；Indian Institute of Technology, Kanpur（印度理工学院坎浦尔）；Department of Electrical Engineering Indian Institute of Technology, Kanpur（电气工程系印度理工学院坎浦尔）；Department of Industrial Engineering Purdue University West Lafayette（工业工程系普渡大学威斯康星拉法叶）
University of Southern California（南加利福尼亚大学）；Facebook Inc.（脸书公司）；Princeton University（普林斯顿大学）；Northwestern University（西北大学）
We study the Safe Reinforcement Learning (SRL) problem using the Constrained Markov Decision Process (CMDP) formulation in which an agent aims to maximize the expected total reward subject to a safety constraint on the expected total value of a utility function. We focus on an episodic setting with the function approximation where the Markov transition kernels have a linear structure but do not impose any additional assumptions on the sampling model. Designing SRL algorithms with provable computational and statistical efficiency is particularly challenging under this setting because of the nee…
Illinois Institute of Technology（伊利诺伊理工学院）；Argonne National Laboratory（阿贡国家实验室）
The canonical solution methodology for finite constrained Markov decision processes (CMDPs), where the objective is to maximize the expected infinite-horizon discounted rewards subject to the expected infinite-horizon discounted costs constraints, is based on convex linear programming. In this brief, we first prove that the optimization objective in the dual linear program of a finite CMDP is a piece-wise linear convex function (PWLC) with respect to the Lagrange penalty multipliers. Next, we propose a novel two-level Gradient-Aware Search (GAS) algorithm which exploits the PWLC structure to f…
We address the problem of finding the optimal policy of a constrained Markov decision process (CMDP) using a gradient descent-based algorithm. Previous results have shown that a primal-dual approach can achieve an $\mathcal{O}(1/\sqrt{T})$ global convergence rate for both the optimality gap and the constraint violation. We propose a new algorithm called policy mirror descent-primal dual (PMD-PD) algorithm that can provably achieve a faster $\mathcal{O}(\log(T)/T)$ convergence rate for both the optimality gap and the constraint violation. For the primal (policy) update, the PMD-PD algorithm uti…
Policy-based Primal-Dual Methods for Concave CMDP with Variance Reduction
Department of Industrial Engineering and Operations Research, UC Berkeley（加州大学伯克利分校工业工程与运筹学系）；Department of Mechanical Engineering, UC Berkeley（加州大学伯克利分校机械工程系）
We propose a successive convex approximation based off-policy optimization (SCAOPO) algorithm to solve the general constrained reinforcement learning problem, which is formulated as a constrained Markov decision process (CMDP) in the context of average cost. The SCAOPO is based on solving a sequence of convex objective/feasibility optimization problems obtained by replacing the objective and constraint functions in the original problems with convex surrogate functions. At each iteration, the convex surrogate problem can be efficiently solved by Lagrange dual method even the policy is parameter…
In the optimization of dynamic systems, the variables typically have constraints. Such problems can be modeled as a Constrained Markov Decision Process (CMDP). This paper considers the peak Constrained Markov Decision Process (PCMDP), where the agent chooses the policy to maximize total reward in the finite horizon as well as satisfy constraints at each epoch with probability 1. We propose a model-free algorithm that converts PCMDP problem to an unconstrained problem and a Q-learning based approach is applied. We define the concept of probably approximately correct (PAC) to the proposed PCMDP …
Constrained Markov decision processes (CMDPs) model scenarios of sequential decision making with multiple objectives that are increasingly important in many applications. However, the model is often unknown and must be learned online while still ensuring the constraint is met, or at least the violation is bounded with time. Some recent papers have made progress on this very challenging problem but either need unsatisfactory assumptions such as knowledge of a safe policy, or have high cumulative regret. We propose the Safe PSRL (posterior sampling-based RL) algorithm that does not need such ass…
We consider large-scale Markov decision processes with an unknown cost function and address the problem of learning a policy from a finite set of expert demonstrations. We assume that the learner is not allowed to interact with the expert and has no access to reinforcement signal of any kind. Existing inverse reinforcement learning methods come with strong theoretical guarantees, but are computationally expensive, while state-of-the-art policy optimization algorithms achieve significant empirical success, but are hampered by limited theoretical understanding. To bridge the gap between theory a…
Simon Fraser University（西蒙弗雷泽大学）；SAIT AI Lab（SAIT人工智能实验室）；Amii（阿尔伯塔机器智能研究所）；University of Alberta（阿尔伯塔大学）；DeepMind（深度思维）；Mila（米拉人工智能研究所）；McGill University（麦吉尔大学）
We study policy optimization in an infinite horizon, $γ$-discounted constrained Markov decision process (CMDP). Our objective is to return a policy that achieves large expected reward with a small constraint violation. We consider the online setting with linear function approximation and assume global access to the corresponding features. We propose a generic primal-dual framework that allows us to bound the reward sub-optimality and constraint violation for arbitrary algorithms in terms of their primal and dual regret on online linear optimization problems. We instantiate this framework to us…
Illinois Institute of Technology（伊利诺伊理工学院）；Argonne National Laboratory（阿贡国家实验室）
In this paper, we apply the Non-Orthogonal Multiple Access (NOMA) technique to improve the massive channel access of a wireless IoT network where solar-powered Unmanned Aerial Vehicles (UAVs) relay data from IoT devices to remote servers. Specifically, IoT devices contend for accessing the shared wireless channel using an adaptive $p$-persistent slotted Aloha protocol; and the solar-powered UAVs adopt Successive Interference Cancellation (SIC) to decode multiple received data from IoT devices to improve access efficiency. To enable an energy-sustainable capacity-optimal network, we study the j…
Instrumental Variable Value Iteration for Causal Offline Reinforcement Learning
Columbia University（哥伦比亚大学）；Northwestern University（西北大学）；Yale University（耶鲁大学）；University of Michigan（密歇根大学）；University of Washington（华盛顿大学）；University of Southern California（南加州大学）
University of Oxford（牛津大学）；Auburn University（奥本大学）
We present GradientDICE for estimating the density ratio between the state distribution of the target policy and the sampling distribution in off-policy reinforcement learning. GradientDICE fixes several problems of GenDICE (Zhang et al., 2020), the state-of-the-art for estimating such density ratios. Namely, the optimization problem in GenDICE is not a convex-concave saddle-point problem once nonlinearity in optimization variable parameterization is introduced to ensure positivity, so any primal-dual algorithm is not guaranteed to converge or find the desired solution. However, such nonlinear…
The Ohio State University（俄亥俄州立大学）；Wayne State University（韦恩州立大学）
We study the constrained reinforcement learning problem, in which an agent aims to maximize the expected cumulative reward subject to a constraint on the expected total value of a utility function. In contrast to existing model-based approaches or model-free methods accompanied with a `simulator', we aim to develop the first model-free, simulator-free algorithm that achieves a sublinear regret and a sublinear constraint violation even in large-scale systems. To this end, we consider the episodic constrained Markov decision processes with linear function approximation, where the transition dyna…
