Robust Q-Learning under Corrupted Rewards

TL;DR

This paper investigates the vulnerability of standard Q-learning to reward corruption attacks and introduces a robust algorithm with proven convergence guarantees that withstands adversarial perturbations in rewards.

Contribution

The paper develops a novel robust Q-learning algorithm that effectively counters reward corruption attacks and provides finite-time convergence guarantees.

Findings

Vanilla Q-learning can be arbitrarily misled by reward corruption.

The proposed robust Q-learning algorithm converges with a rate similar to non-adversarial settings.

The method remains effective even with rewards having infinite support but bounded second moments.

Abstract

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.