Cancellation-Free Regret Bounds for Lagrangian Approaches in Constrained Markov Decision Processes

• URL: http://arxiv.org/abs/2306.07001v2
• Date: Wed, 30 Aug 2023 15:58:45 GMT
• Title: Cancellation-Free Regret Bounds for Lagrangian Approaches in Constrained Markov Decision Processes
• Authors: Adrian M\"uller, Pragnya Alatur, Giorgia Ramponi, Niao He
• Abstract summary: We propose a novel model-based dual algorithm OptAug-CMDP for finite-horizon CMDPs. Our algorithm achieves a regret without the need for the cancellation of errors.
• Score: 24.51454563844664
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Constrained Markov Decision Processes (CMDPs) are one of the common ways to model safe reinforcement learning problems, where constraint functions model the safety objectives. Lagrangian-based dual or primal-dual algorithms provide efficient methods for learning in CMDPs. For these algorithms, the currently known regret bounds in the finite-horizon setting allow for a "cancellation of errors"; one can compensate for a constraint violation in one episode with a strict constraint satisfaction in another. However, we do not consider such a behavior safe in practical applications. In this paper, we overcome this weakness by proposing a novel model-based dual algorithm OptAug-CMDP for tabular finite-horizon CMDPs. Our algorithm is motivated by the augmented Lagrangian method and can be performed efficiently. We show that during $K$ episodes of exploring the CMDP, our algorithm obtains a regret of $\tilde{O}(\sqrt{K})$ for both the objective and the constraint violation. Unlike existing Lagrangian approaches, our algorithm achieves this regret without the need for the cancellation of errors.

Related papers

• Learning Constrained Markov Decision Processes With Non-stationary Rewards and Constraints [34.7178680288326]
  In constrained Markov decision processes (CMDPs) with adversarial rewards and constraints, a well-known impossibility result prevents any algorithm from attaining sublinear regret and sublinear constraint violation. We show that this negative result can be eased in CMDPs with non-stationary rewards and constraints, by providing algorithms whose performances smoothly degrade as non-stationarity increases.
  arXiv  Detail & Related papers  (2024-05-23T09:48:48Z)
• Learning Adversarial MDPs with Stochastic Hard Constraints [37.24692425018]
  We study online learning problems in constrained decision processes with adversarial losses and hard constraints. We design an algorithm that achieves sublinear regret while ensuring that the constraints are satisfied at every episode with high probability.
  arXiv  Detail & Related papers  (2024-03-06T12:49:08Z)
• Truly No-Regret Learning in Constrained MDPs [61.78619476991494]
  We propose a model-based primal-dual algorithm to learn in an unknown CMDP. We prove that our algorithm achieves sublinear regret without error cancellations.
  arXiv  Detail & Related papers  (2024-02-24T09:47:46Z)
• A Unifying Framework for Online Optimization with Long-Term Constraints [62.35194099438855]
  We study online learning problems in which a decision maker has to take a sequence of decisions subject to $m$ long-term constraints. The goal is to maximize their total reward, while at the same time achieving small cumulative violation across the $T$ rounds. We present the first best-of-both-world type algorithm for this general class problems, with no-regret guarantees both in the case in which rewards and constraints are selected according to an unknown model, and in the case in which they are selected at each round by an adversary.
  arXiv  Detail & Related papers  (2022-09-15T16:59:19Z)
• Learning Infinite-Horizon Average-Reward Markov Decision Processes with Constraints [39.715977181666766]
  We study regret for infinite-horizon average-reward Markov Decision Processes (MDPs) under cost constraints. Our algorithm ensures $widetildeO(sqrtT)$ regret and constant constraint violation for ergodic MDPs. These are the first set of provable algorithms for weakly communicating MDPs with cost constraints.
  arXiv  Detail & Related papers  (2022-01-31T23:52:34Z)
• Safe Online Bid Optimization with Return-On-Investment and Budget Constraints subject to Uncertainty [87.81197574939355]
  We study the nature of both the optimization and learning problems. We provide an algorithm, namely GCB, guaranteeing sublinear regret at the cost of a potentially linear number of constraints violations. More interestingly, we provide an algorithm, namely GCB_safe(psi,phi), guaranteeing both sublinear pseudo-regret and safety w.h.p. at the cost of accepting tolerances psi and phi.
  arXiv  Detail & Related papers  (2022-01-18T17:24:20Z)
• Misspecified Gaussian Process Bandit Optimization [59.30399661155574]
  Kernelized bandit algorithms have shown strong empirical and theoretical performance for this problem. We introduce a emphmisspecified kernelized bandit setting where the unknown function can be $epsilon$--uniformly approximated by a function with a bounded norm in some Reproducing Kernel Hilbert Space (RKHS) We show that our algorithm achieves optimal dependence on $epsilon$ with no prior knowledge of misspecification.
  arXiv  Detail & Related papers  (2021-11-09T09:00:02Z)
• A Stochastic Composite Augmented Lagrangian Method For Reinforcement Learning [9.204659134755795]
  We consider the linear programming (LP) formulation for deep reinforcement learning. The augmented Lagrangian method suffers the double-sampling obstacle in solving the LP. A deep parameterized augment Lagrangian method is proposed.
  arXiv  Detail & Related papers  (2021-05-20T13:08:06Z)
• Exploration-Exploitation in Constrained MDPs [79.23623305214275]
  We investigate the exploration-exploitation dilemma in Constrained Markov Decision Processes (CMDPs) While learning in an unknown CMDP, an agent should trade-off exploration to discover new information about the MDP. While the agent will eventually learn a good or optimal policy, we do not want the agent to violate the constraints too often during the learning process.
  arXiv  Detail & Related papers  (2020-03-04T17:03:56Z)
• Upper Confidence Primal-Dual Reinforcement Learning for CMDP with Adversarial Loss [145.54544979467872]
  We consider online learning for episodically constrained Markov decision processes (CMDPs) We propose a new emphupper confidence primal-dual algorithm, which only requires the trajectories sampled from the transition model. Our analysis incorporates a new high-probability drift analysis of Lagrange multiplier processes into the celebrated regret analysis of upper confidence reinforcement learning.
  arXiv  Detail & Related papers  (2020-03-02T05:02:23Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.