arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2409.03237cs.LGcs.SYeess.SYmath.OCstat.ML
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损坏奖励下的鲁棒Q学习

Robust Q-Learning under Corrupted Rewards

North Carolina State University(北卡罗来纳州立大学)

Sreejeet Maity, Aritra Mitra

AI总结:

本文研究Q学习在奖励被对抗性污染下的鲁棒性问题,提出一种利用历史奖励数据构造鲁棒经验贝尔曼算子的同步Q学习算法,并证明其有限时间收敛速率与无攻击时的最优界限匹配,仅相差一个随污染比例缩放的不可避免误差项。

摘要:

近年来,分析无模型强化学习算法的非渐近行为引起了广泛关注。然而,此类算法在非理想环境(例如存在损坏奖励)中的性能尚不为人所充分理解。受这一研究空白的推动,我们研究了著名的Q学习算法在强污染攻击模型下的鲁棒性,在该模型中,对手可以任意扰动一小部分观测到的奖励。我们首先证明,这种攻击可以使普通Q学习算法产生任意大的误差。随后,我们开发了一种新颖的鲁棒同步Q学习算法,该算法在每个时间步利用历史奖励数据构造鲁棒的经验贝尔曼算子。最后,我们证明了该算法的有限时间收敛速率,该速率与已知的最先进界限(在无攻击情况下)相匹配,仅相差一个不可避免的小的 $O(\varepsilon)$ 误差项,该误差项随对抗污染比例 $\varepsilon$ 缩放。值得注意的是,即使真实奖励分布具有无限支撑,只要它们具有有界的二阶矩,我们的结果仍然成立。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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