Uniform-PAC Guarantees for Model-Based RL with Bounded Eluder Dimension

Yue Wu, Jiafan He, Quanquan Gu

Keywords: reinforcement learning, bandit, eluder dimension

TL;DR: We propose uniform-PAC, model-based algorithms for both bandit and episodic RL with the notion of eluder dimension.

Abstract: Recently, there has been remarkable progress in reinforcement learning (RL) with general function approximation. However, all these works only provide regret or sample complexity guarantees. It is still an open question if one can achieve stronger performance guarantees, i.e., the uniform probably approximate correctness (Uniform-PAC) guarantee that can imply both a sub-linear regret bound and a polynomial sample complexity for any target learning accuracy. We study this problem by proposing algorithms for both nonlinear bandits and model-based episodic RL using the general function class with a bounded eluder dimension. The key idea of the proposed algorithms is to assign each action to different levels according to its width with respect to the confidence set. The achieved uniform-PAC sample complexity is tight in the sense that it matches the state-of-the-art regret bounds or sample complexity guarantees when reduced to the linear case. To the best of our knowledge, this is the first work for uniform-PAC guarantees on bandit and RL that goes beyond linear cases.