The Best of Both Worlds: Reinforcement Learning with Logarithmic Regret and Policy Switches
This work addresses the challenge of efficient and adaptive learning in RL for researchers and practitioners, offering instance-dependent guarantees that are incremental over prior instance-independent results.
The paper tackles the problem of achieving logarithmic regret in episodic reinforcement learning with general function classes, showing that algorithms can achieve O(log T) regret with O(log T) policy switches when there is an action gap in every state, and provides matching lower bounds.
In this paper, we study the problem of regret minimization for episodic Reinforcement Learning (RL) both in the model-free and the model-based setting. We focus on learning with general function classes and general model classes, and we derive results that scale with the eluder dimension of these classes. In contrast to the existing body of work that mainly establishes instance-independent regret guarantees, we focus on the instance-dependent setting and show that the regret scales logarithmically with the horizon $T$, provided that there is a gap between the best and the second best action in every state. In addition, we show that such a logarithmic regret bound is realizable by algorithms with $O(\log T)$ switching cost (also known as adaptivity complexity). In other words, these algorithms rarely switch their policy during the course of their execution. Finally, we complement our results with lower bounds which show that even in the tabular setting, we cannot hope for regret guarantees lower than $o(\log T)$.