Near-Constant Strong Violation and Last-Iterate Convergence for Online CMDPs via Decaying Safety Margins

TL;DR

This paper introduces FlexDOME, a novel algorithm for safe online reinforcement learning in CMDPs, achieving near-constant constraint violations and sublinear regret through innovative safety margin scheduling and convergence analysis.

Contribution

The paper presents the first provably near-constant violation and last-iterate convergence algorithm for safe online CMDPs using time-varying safety margins.

Findings

FlexDOME achieves near-constant constraint violation.

FlexDOME guarantees sublinear regret.

Experiments validate theoretical guarantees.

Abstract

We study safe online reinforcement learning in Constrained Markov Decision Processes (CMDPs) under strong regret and violation metrics, which forbid error cancellation over time. Existing primal-dual methods that achieve sublinear strong reward regret inevitably incur growing strong constraint violation or are restricted to average-iterate convergence due to inherent oscillations. To address these limitations, we propose the Flexible safety Domain Optimization via Margin-regularized Exploration (FlexDOME) algorithm, the first to provably achieve near-constant $\tilde{O}(1)$ strong constraint violation alongside sublinear strong regret and non-asymptotic last-iterate convergence. FlexDOME incorporates time-varying safety margins and regularization terms into the primal-dual framework. Our theoretical analysis relies on a novel term-wise asymptotic dominance strategy, where the safety margin is rigorously scheduled to asymptotically majorize the functional decay rates of the optimization and statistical errors, thereby clamping cumulative violations to a near-constant level. Furthermore, we establish non-asymptotic last-iterate convergence guarantees via a policy-dual Lyapunov argument. Experiments corroborate our theoretical findings.