  We initiate the study of multi-stage episodic reinforcement learning under
adversarial corruptions in both the rewards and the transition probabilities of
the underlying system extending recent results for the special case of
stochastic bandits. We provide a framework which modifies the aggressive
exploration enjoyed by existing reinforcement learning approaches based on
"optimism in the face of uncertainty", by complementing them with principles
from "action elimination". Importantly, our framework circumvents the major
challenges posed by naively applying action elimination in the RL setting, as
formalized by a lower bound we demonstrate. Our framework yields efficient
algorithms which (a) attain near-optimal regret in the absence of corruptions
and (b) adapt to unknown levels corruption, enjoying regret guarantees which
degrade gracefully in the total corruption encountered. To showcase the
generality of our approach, we derive results for both tabular settings (where
states and actions are finite) as well as linear-function-approximation
settings (where the dynamics and rewards admit a linear underlying
representation). Notably, our work provides the first sublinear regret
guarantee which accommodates any deviation from purely i.i.d. transitions in
the bandit-feedback model for episodic reinforcement learning.
