Coordinated Attacks against Contextual Bandits: Fundamental Limits and Defense Mechanisms
Jeongyeol Kwon, Yonathan Efroni, Constantine Caramanis, Shie Mannor
Abstract
Motivated by online recommendation systems, we propose the problem of finding the optimal policy in multitask contextual bandits when a small fraction $\alpha < 1/2$ 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 $O(1/\epsilon^2)$ 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 $\tilde{\Omega}(\min(S,A) \cdot \alpha^2 / \epsilon^2)$
BibTeX
@InProceedings{pmlr-v162-kwon22a,
title = {Coordinated Attacks against Contextual Bandits: Fundamental Limits and Defense Mechanisms},
author = {Kwon, Jeongyeol and Efroni, Yonathan and Caramanis, Constantine and Mannor, Shie},
booktitle = {Proceedings of the 39th International Conference on Machine Learning},
pages = {11772--11789},
year = {2022},
editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan},
volume = {162},
series = {Proceedings of Machine Learning Research},
month = {17--23 Jul},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v162/kwon22a/kwon22a.pdf},
url = {https://proceedings.mlr.press/v162/kwon22a.html},
abstract = {Motivated by online recommendation systems, we propose the problem of finding the optimal policy in multitask contextual bandits when a small fraction $\alpha < 1/2$ 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 $O(1/\epsilon^2)$ 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 $\tilde{\Omega}(\min(S,A) \cdot \alpha^2 / \epsilon^2)$