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arXiv 2008.09312cs.LGstat.ML
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随机多臂老虎机上的近最优对抗攻击与平滑响应防御

Near Optimal Adversarial Attacks on Stochastic Bandits and Defenses with Smoothed Responses

University of Illinois Urbana-Champaign(伊利诺伊大学厄巴纳-香槟分校)

Shiliang Zuo

AI总结:

本文研究随机多臂老虎机中的对抗攻击与防御,提出针对UCB和汤普森采样的近最优攻击策略,并设计两种简单防御算法,使竞争比任意接近1。

摘要:

我研究了针对随机多臂老虎机算法的对抗性攻击。在每一轮中,学习者选择一个臂,并生成一个随机奖励。对手策略性地向奖励中添加扰动,而学习者每轮只能观察到被扰动的奖励。本文提出了两组结果。第一组研究对手的最优攻击策略。对手有一个希望推广的目标臂,其目标是操纵学习者选择该目标臂 $T - o(T)$ 次。我针对UCB和汤普森采样设计了攻击策略,其成本仅为 $\widehat{O}(\sqrt{\log T})$。本文给出了匹配的下界,并精确刻画了UCB、汤普森采样和 $\varepsilon$-贪心算法的脆弱性。第二组研究学习者如何防御对手。受平滑分析和行为经济学文献的启发,我提出了两种简单算法,其竞争比可任意接近1。

英文摘要:

I study adversarial attacks against stochastic bandit algorithms. At each round, the learner chooses an arm, and a stochastic reward is generated. The adversary strategically adds corruption to the reward, and the learner is only able to observe the corrupted reward at each round. Two sets of results are presented in this paper. The first set studies the optimal attack strategies for the adversary. The adversary has a target arm he wishes to promote, and his goal is to manipulate the learner into choosing this target arm $T - o(T)$ times. I design attack strategies against UCB and Thompson Sampling that only spend $\widehat{O}(\sqrt{\log T})$ cost. Matching lower bounds are presented, and the vulnerability of UCB, Thompson sampling, and $\varepsilon$-greedy are exactly characterized. The second set studies how the learner can defend against the adversary. Inspired by literature on smoothed analysis and behavioral economics, I present two simple algorithms that achieve a competitive ratio arbitrarily close to 1.

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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