  This study tackles the challenges of adversarial corruption in model-based
reinforcement learning (RL), where the transition dynamics can be corrupted by
an adversary. Existing studies on corruption-robust RL mostly focus on the
setting of model-free RL, where robust least-square regression is often
employed for value function estimation. However, these techniques cannot be
directly applied to model-based RL. In this paper, we focus on model-based RL
and take the maximum likelihood estimation (MLE) approach to learn transition
model. Our work encompasses both online and offline settings. In the online
setting, we introduce an algorithm called corruption-robust optimistic MLE
(CR-OMLE), which leverages total-variation (TV)-based information ratios as
uncertainty weights for MLE. We prove that CR-OMLE achieves a regret of
$\tilde{\mathcal{O}}(\sqrt{T} + C)$, where $C$ denotes the cumulative
corruption level after $T$ episodes. We also prove a lower bound to show that
the additive dependence on $C$ is optimal. We extend our weighting technique to
the offline setting, and propose an algorithm named corruption-robust
pessimistic MLE (CR-PMLE). Under a uniform coverage condition, CR-PMLE exhibits
suboptimality worsened by $\mathcal{O}(C/n)$, nearly matching the lower bound.
To the best of our knowledge, this is the first work on corruption-robust
model-based RL algorithms with provable guarantees.
