A repeated retraining algorithm with robust gradient estimation converges to an approximately stable policy in performative RL under Huber contamination, with approximation error scaling as the square root of the corruption level.
Regret Bound by Variation for Online Convex Optimization
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abstract
In citep{Hazan-2008-extract}, the authors showed that the regret of online linear optimization can be bounded by the total variation of the cost vectors. In this paper, we extend this result to general online convex optimization. We first analyze the limitations of the algorithm in \citep{Hazan-2008-extract} when applied it to online convex optimization. We then present two algorithms for online convex optimization whose regrets are bounded by the variation of cost functions. We finally consider the bandit setting, and present a randomized algorithm for online bandit convex optimization with a variation-based regret bound. We show that the regret bound for online bandit convex optimization is optimal when the variation of cost functions is independent of the number of trials.
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On Corruption-Robustness in Performative Reinforcement Learning
A repeated retraining algorithm with robust gradient estimation converges to an approximately stable policy in performative RL under Huber contamination, with approximation error scaling as the square root of the corruption level.