Robust Q-Learning under Corrupted Rewards
<|reference_start|>Robust Q-Learning under Corrupted Rewards: 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.<|reference_end|>
@article{maity2024robust,
    title={Robust Q-Learning under Corrupted Rewards},
    author={Sreejeet Maity and Aritra Mitra},
    journal={arXiv preprint arXiv:2409.03237},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.03237},
    primaryClass={cs.LG cs.SY eess.SY math.OC stat.ML}
}