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.

本研究提出了针对非线性赌博机和基于模型的的情境强化学习的算法，使用有界eluder维数的通用函数类，通过将每个行为分配到不同的级别，从而实现了统一的概率近似正确性（Uniform-PAC）保证。

具有有限逃避者维度的基于模型的RL的均匀PAC保证