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We study model-free reinforcement learning (RL) algorithms in episodicnon-stationary constrained Markov Decision Processes (CMDPs), in which an agentaims to maximize the expected cumulative reward subject to a cumulativeconstraint on the expected utility (cost). In the non-stationary environment,reward, utility functions, and transition kernels can vary arbitrarily overtime as long as the cumulative variations do not exceed certain variationbudgets. We propose the first model-free, simulator-free RL algorithms withsublinear regret and zero constraint violation for non-stationary CMDPs in bothtabular and linear function approximation settings with provable performanceguarantees. Our results on regret bound and constraint violation for thetabular case match the corresponding best results for stationary CMDPs when thetotal budget is known. Additionally, we present a general framework foraddressing the well-known challenges associated with analyzing non-stationaryCMDPs, without requiring prior knowledge of the variation budget. We apply theapproach for both tabular and linear approximation settings.

Provably Efficient Model-Free Algorithms for Non-stationary CMDPs