Despite the significant interest and progress in reinforcement learning (RL) problems with adversarial corruption, current works are either confined to the linear setting or lead to an undesired $\tilde{O}(\sqrt{T}\zeta)$ regret bound, where $T$ is the number of rounds and $\zeta$ is the total amount of corruption. In this paper, we consider the contextual bandit with general function approximation and propose a computationally efficient algorithm to achieve a regret of $\tilde{O}(\sqrt{T}+\zeta)$. The proposed algorithm relies on the recently developed uncertainty-weighted least-squares regression from linear contextual bandit and a new weighted estimator of uncertainty for the general function class. In contrast to the existing analysis that heavily relies on the linear structure, we develop a novel technique to control the sum of weighted uncertainty, thus establishing the final regret bounds. We then generalize our algorithm to the episodic MDP setting and first achieve an additive dependence on the corruption level $\zeta$ in the scenario of general function approximation. Notably, our algorithms achieve regret bounds either nearly match the performance lower bound or improve the existing methods for all the corruption levels and in both known and unknown $\zeta$ cases.

翻译：尽管强化学习在对抗性腐败问题中取得了显著进展与关注，现有工作要么局限于线性设定，要么导致次优的$\tilde{O}(\sqrt{T}\zeta)$遗憾界，其中$T$为回合数，$\zeta$为总腐败量。本文考虑具有通用函数逼近的上下文赌博机，提出一种计算高效的算法，其遗憾界为$\tilde{O}(\sqrt{T}+\zeta)$。该算法基于线性上下文赌博机中近期发展的不确定性加权最小二乘回归，以及针对通用函数类的新加权不确定性估计器。与现有高度依赖线性结构的分析不同，我们开发了一种控制加权不确定性总和的新技术，从而确立最终遗憾界。随后，我们将算法推广至情节式马尔可夫决策过程设定，首次在通用函数逼近场景下实现了对腐败水平$\zeta$的加性依赖。值得注意的是，我们的算法在所有腐败水平及已知/未知$\zeta$情形下的遗憾界，或近乎匹配性能下界，或优于现有方法。