Near-Optimal Goal-Oriented Reinforcement Learning in Non-Stationary Environments

Part of Advances in Neural Information Processing Systems 35 (NeurIPS 2022) Main Conference Track

Authors

Liyu Chen, Haipeng Luo

Abstract

We initiate the study of dynamic regret minimization for goal-oriented reinforcement learning modeled by a non-stationary stochastic shortest path problem with changing cost and transition functions.We start by establishing a lower bound $\Omega((B_{\star} SAT_{\star}(\Delta_c + B_{\star}^2\Delta_P))^{1/3}K^{2/3})$, where $B_{\star}$ is the maximum expected cost of the optimal policy of any episode starting from any state, $T_{\star}$ is the maximum hitting time of the optimal policy of any episode starting from the initial state, $SA$ is the number of state-action pairs, $\Delta_c$ and $\Delta_P$ are the amount of changes of the cost and transition functions respectively, and $K$ is the number of episodes.The different roles of $\Delta_c$ and $\Delta_P$ in this lower bound inspire us to design algorithms that estimate costs and transitions separately.Specifically, assuming the knowledge of $\Delta_c$ and $\Delta_P$, we develop a simple but sub-optimal algorithm and another more involved minimax optimal algorithm (up to logarithmic terms).These algorithms combine the ideas of finite-horizon approximation [Chen et al., 2021b], special Bernstein-style bonuses of the MVP algorithm [Zhang et al., 2020], adaptive confidence widening [Wei and Luo, 2021], as well as some new techniques such as properly penalizing long-horizon policies.Finally, when $\Delta_c$ and $\Delta_P$ are unknown, we develop a variant of the MASTER algorithm [Wei and Luo, 2021] and integrate the aforementioned ideas into it to achieve $\widetilde{O}(\min\{B_{\star} S\sqrt{ALK}, (B_{\star}^2S^2AT_{\star}(\Delta_c+B_{\star}\Delta_P))^{1/3}K^{2/3}\})$ regret, where $L$ is the unknown number of changes of the environment.