A Model Selection Approach for Corruption Robust Reinforcement Learning
This addresses robustness in RL for applications like robotics or finance where data corruption is a concern, representing a significant theoretical advance rather than an incremental improvement.
The paper tackles reinforcement learning with adversarial corruption in transitions and rewards by developing a model selection approach, achieving worst-case optimal regret bounds without prior knowledge of corruption for tabular MDPs and improved bounds for linear MDPs.
We develop a model selection approach to tackle reinforcement learning with adversarial corruption in both transition and reward. For finite-horizon tabular MDPs, without prior knowledge on the total amount of corruption, our algorithm achieves a regret bound of $\widetilde{\mathcal{O}}(\min\{\frac{1}Δ, \sqrt{T}\}+C)$ where $T$ is the number of episodes, $C$ is the total amount of corruption, and $Δ$ is the reward gap between the best and the second-best policy. This is the first worst-case optimal bound achieved without knowledge of $C$, improving previous results of Lykouris et al. (2021); Chen et al. (2021); Wu et al. (2021). For finite-horizon linear MDPs, we develop a computationally efficient algorithm with a regret bound of $\widetilde{\mathcal{O}}(\sqrt{(1+C)T})$, and another computationally inefficient one with $\widetilde{\mathcal{O}}(\sqrt{T}+C)$, improving the result of Lykouris et al. (2021) and answering an open question by Zhang et al. (2021b). Finally, our model selection framework can be easily applied to other settings including linear bandits, linear contextual bandits, and MDPs with general function approximation, leading to several improved or new results.