arXiv:2502.04662cs.LGcs.SY2025-02中稿 · AISTATS 2025被引 6

提出抗干扰的强化学习算法,让模型在数据被篡改时仍能准确估计长期回报。

Adversarially-Robust TD Learning with Markovian Data: Finite-Time Rates and Fundamental Limits

  • 设计鲁棒TD算法,用中位数均值法应对奖励数据被恶意污染。
  • 证明算法在有限步内收敛速度接近经典方法,仅多出ε的误差项。
  • 首次揭示此类抗干扰算法的理论极限,适合高风险场景研究者。

强化学习中的策略评估问题旨在估计给定策略的长期回报(价值函数)。经典的时序差分(TD)学习算法解决了这一问题,近期研究已建立其有限时间收敛性。然而,这些保证依赖于奖励观测来自理想分布(如亚高斯分布)。在真实环境中,这种理想假设可能不成立。本文从对抗鲁棒性角度重新审视该问题,考虑霍伯尔(Huber)污染奖励模型——敌手以小概率ε任意篡改每条奖励样本。我们发现,标准TD算法会因此收敛至任意错误值。为此,提出新算法Robust-TD,证明其有限时间性能与线性函数近似下的经典TD相当,仅多出一个可忽略的O(ε)项,反映污染影响。进一步给出极小极大下界,表明该误差项不可避免。这是首个针对马尔可夫噪声驱动的随机逼近方案的对抗鲁棒性结果。关键技术是分析受污染、具有时间相关性的中位数均值估计器,对鲁棒统计学亦具独立意义。

原文摘要 · Abstract (English)

One of the most basic problems in reinforcement learning (RL) is policy evaluation: estimating the long-term return, i.e., value function, corresponding to a given fixed policy. The celebrated Temporal Difference (TD) learning algorithm addresses this problem, and recent work has investigated finite-time convergence guarantees for this algorithm and variants thereof. However, these guarantees hinge on the reward observations being always generated from a well-behaved (e.g., sub-Gaussian) true reward distribution. Motivated by harsh, real-world environments where such an idealistic assumption may no longer hold, we revisit the policy evaluation problem from the perspective of adversarial robustness. In particular, we consider a Huber-contaminated reward model where an adversary can arbitrarily corrupt each reward sample with a small probability $ε$. Under this observation model, we first show that the adversary can cause the vanilla TD algorithm to converge to any arbitrary value function. We then develop a novel algorithm called Robust-TD and prove that its finite-time guarantees match that of vanilla TD with linear function approximation up to a small $O(ε)$ term that captures the effect of corruption. We complement this result with a minimax lower bound, revealing that such an additive corruption-induced term is unavoidable. To our knowledge, these results are the first of their kind in the context of adversarial robustness of stochastic approximation schemes driven by Markov noise. The key new technical tool that enables our results is an analysis of the Median-of-Means estimator with corrupted, time-correlated data that might be of independent interest to the literature on robust statistics.

强化学习鲁棒性对抗攻击价值估计

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