Adversarial Attacks on Combinatorial Multi-Armed Bandits

TL;DR

This paper investigates the vulnerability of combinatorial multi-armed bandits to reward poisoning attacks, establishing conditions for attackability, proposing an attack algorithm, and analyzing the impact of knowledge about the bandit instance.

Contribution

It introduces a comprehensive attackability condition for CMAB, reveals the dependence of attack success on adversary knowledge, and validates findings through extensive experiments.

Findings

Attackability depends on reward and outcome distributions.

Knowledge of the bandit instance affects attack success.

Attacks are more challenging when the environment is unknown.

Abstract

We study reward poisoning attacks on Combinatorial Multi-armed Bandits (CMAB). We first provide a sufficient and necessary condition for the attackability of CMAB, a notion to capture the vulnerability and robustness of CMAB. The attackability condition depends on the intrinsic properties of the corresponding CMAB instance such as the reward distributions of super arms and outcome distributions of base arms. Additionally, we devise an attack algorithm for attackable CMAB instances. Contrary to prior understanding of multi-armed bandits, our work reveals a surprising fact that the attackability of a specific CMAB instance also depends on whether the bandit instance is known or unknown to the adversary. This finding indicates that adversarial attacks on CMAB are difficult in practice and a general attack strategy for any CMAB instance does not exist since the environment is mostly unknown to the adversary. We validate our theoretical findings via extensive experiments on real-world CMAB applications including probabilistic maximum covering problem, online minimum spanning tree, cascading bandits for online ranking, and online shortest path.