Coordinated Attacks against Contextual Bandits: Fundamental Limits and Defense Mechanisms

Jeongyeol Kwon, Yonathan Efroni, Constantine Caramanis, Shie Mannor

Research output: Contribution to journalConference articlepeer-review

Abstract

Motivated by online recommendation systems, we propose the problem of finding the optimal policy in multitask contextual bandits when a small fraction α < 1/2 of tasks (users) are arbitrary and adversarial. The remaining fraction of good users share the same instance of contextual bandits with S contexts and A actions (items). Naturally, whether a user is good or adversarial is not known in advance. The goal is to robustly learn the policy that maximizes rewards for good users with as few user interactions as possible. Without adversarial users, established results in collaborative filtering show that O(1/ϵ2) per-user interactions suffice to learn a good policy, precisely because information can be shared across users. This parallelization gain is fundamentally altered by the presence of adversarial users: unless there are super-polynomial number of users, we show a lower bound of Ω(equation presented)(min(S, A) · α2/ϵ2) per-user interactions to learn an ϵ-optimal policy for the good users. We then show we can achieve an Õ(min(S, A) · α/ϵ2) upper-bound, by employing efficient robust mean estimators for both uni-variate and high-dimensional random variables. We also show that this can be improved depending on the distributions of contexts.

Original languageEnglish
Pages (from-to)11772-11789
Number of pages18
JournalProceedings of Machine Learning Research
Volume162
StatePublished - 2022
Event39th International Conference on Machine Learning, ICML 2022 - Baltimore, United States
Duration: 17 Jul 202223 Jul 2022
https://proceedings.mlr.press/v162/

All Science Journal Classification (ASJC) codes

  • Software
  • Artificial Intelligence
  • Control and Systems Engineering
  • Statistics and Probability

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