Robust Q-Learning under Corrupted Rewards
This addresses robustness in reinforcement learning for applications in non-ideal environments, such as adversarial settings, but is incremental as it builds on existing Q-learning frameworks.
The paper tackles the problem of Q-learning's vulnerability to corrupted rewards by developing a robust algorithm that uses historical data to construct robust empirical Bellman operators, achieving a finite-time convergence rate that matches state-of-the-art bounds up to an O(ε) error term scaling with the corruption fraction ε.
Recently, there has been a surge of interest in analyzing the non-asymptotic behavior of model-free reinforcement learning algorithms. However, the performance of such algorithms in non-ideal environments, such as in the presence of corrupted rewards, is poorly understood. Motivated by this gap, we investigate the robustness of the celebrated Q-learning algorithm to a strong-contamination attack model, where an adversary can arbitrarily perturb a small fraction of the observed rewards. We start by proving that such an attack can cause the vanilla Q-learning algorithm to incur arbitrarily large errors. We then develop a novel robust synchronous Q-learning algorithm that uses historical reward data to construct robust empirical Bellman operators at each time step. Finally, we prove a finite-time convergence rate for our algorithm that matches known state-of-the-art bounds (in the absence of attacks) up to a small inevitable $O(\varepsilon)$ error term that scales with the adversarial corruption fraction $\varepsilon$. Notably, our results continue to hold even when the true reward distributions have infinite support, provided they admit bounded second moments.