  We study episodic reinforcement learning under unknown adversarial
corruptions in both the rewards and the transition probabilities of the
underlying system. We propose new algorithms which, compared to the existing
results in (Lykouris et al., 2020), achieve strictly better regret bounds in
terms of total corruptions for the tabular setting. To be specific, firstly,
our regret bounds depend on more precise numerical values of total rewards
corruptions and transition corruptions, instead of only on the total number of
corrupted episodes. Secondly, our regret bounds are the first of their kind in
the reinforcement learning setting to have the number of corruptions show up
additively with respect to $\min\{\sqrt{T}, \text{PolicyGapComplexity}\}$
rather than multiplicatively. Our results follow from a general algorithmic
framework that combines corruption-robust policy elimination meta-algorithms,
and plug-in reward-free exploration sub-algorithms. Replacing the
meta-algorithm or sub-algorithm may extend the framework to address other
corrupted settings with potentially more structure.
