Sample Complexity of an Adversarial Attack on UCB-based Best-arm Identification Policy

• URL: http://arxiv.org/abs/2209.05692v1
• Date: Tue, 13 Sep 2022 02:31:30 GMT
• Title: Sample Complexity of an Adversarial Attack on UCB-based Best-arm Identification Policy
• Authors: Varsha Pendyala
• Abstract summary: I study the problem of adversarial perturbations to rewards, in a Multi-armed bandit (MAB) setting. I focus on an adversarial attack to a UCB type best-arm identification policy applied to a MAB.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: In this work I study the problem of adversarial perturbations to rewards, in a Multi-armed bandit (MAB) setting. Specifically, I focus on an adversarial attack to a UCB type best-arm identification policy applied to a stochastic MAB. The UCB attack presented in [1] results in pulling a target arm K very often. I used the attack model of [1] to derive the sample complexity required for selecting target arm K as the best arm. I have proved that the stopping condition of UCB based best-arm identification algorithm given in [2], can be achieved by the target arm K in T rounds, where T depends only on the total number of arms and $\sigma$ parameter of $\sigma^2-$ sub-Gaussian random rewards of the arms.

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