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Despite the significant interest and progress in reinforcement learning (RL)problems with adversarial corruption, current works are either confined to thelinear 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 ofcorruption. In this paper, we consider the contextual bandit with generalfunction approximation and propose a computationally efficient algorithm toachieve a regret of $\tilde{O}(\sqrt{T}+\zeta)$. The proposed algorithm relieson the recently developed uncertainty-weighted least-squares regression fromlinear contextual bandit and a new weighted estimator of uncertainty for thegeneral function class. In contrast to the existing analysis that heavilyrelies on the linear structure, we develop a novel technique to control the sumof weighted uncertainty, thus establishing the final regret bounds. We thengeneralize our algorithm to the episodic MDP setting and first achieve anadditive dependence on the corruption level $\zeta$ in the scenario of generalfunction approximation. Notably, our algorithms achieve regret bounds eithernearly match the performance lower bound or improve the existing methods forall the corruption levels and in both known and unknown $\zeta$ cases.

Corruption-Robust Algorithms with Uncertainty Weighting for Nonlinear Contextual Bandits and Markov Decision Processes