Robust Q-Learning under Corrupted Rewards
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910590472028160 |
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| author | Maity, Sreejeet Mitra, Aritra |
| author_facet | Maity, Sreejeet Mitra, Aritra |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_03237 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Robust Q-Learning under Corrupted Rewards Maity, Sreejeet Mitra, Aritra Machine Learning Systems and Control Optimization and Control 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. |
| title | Robust Q-Learning under Corrupted Rewards |
| topic | Machine Learning Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2409.03237 |