Provably Efficient Primal-Dual Reinforcement Learning for CMDPs with Non-stationary Objectives and Constraints
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We consider primal-dual-based reinforcement learning (RL) in episodic constrained Markov decision processes (CMDPs) with non-stationary objectives and constraints, which play 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 propose a Periodically Restarted Optimistic Primal-Dual Proximal Policy Optimization (PROPD-PPO) algorithm that features three mechanisms: periodic-restart-based policy improvement, dual update with dual regularization, and periodic-restart-based optimistic policy evaluation. We establish a dynamic regret bound and a constraint violation bound for the proposed algorithm in both the linear kernel CMDP function approximation setting and the tabular CMDP setting. This paper provides the first provably efficient algorithm for non-stationary CMDPs with safe exploration.
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