When Are Linear Stochastic Bandits Attackable?
Huazheng Wang, Haifeng Xu, Hongning Wang
Abstract
We study adversarial attacks on linear stochastic bandits: by manipulating the rewards, an adversary aims to control the behaviour of the bandit algorithm. Perhaps surprisingly, we first show that some attack goals can never be achieved. This is in a sharp contrast to context-free stochastic bandits, and is intrinsically due to the correlation among arms in linear stochastic bandits. Motivated by this finding, this paper studies the attackability of a $k$-armed linear bandit environment. We first provide a complete necessity and sufficiency characterization of attackability based on the geometry of the arms’ context vectors. We then propose a two-stage attack method against LinUCB and Robust Phase Elimination. The method first asserts whether the given environment is attackable; and if yes, it poisons the rewards to force the algorithm to pull a target arm linear times using only a sublinear cost. Numerical experiments further validate the effectiveness and cost-efficiency of the proposed attack method.
BibTeX
@InProceedings{pmlr-v162-wang22ai,
title = {When Are Linear Stochastic Bandits Attackable?},
author = {Wang, Huazheng and Xu, Haifeng and Wang, Hongning},
booktitle = {Proceedings of the 39th International Conference on Machine Learning},
pages = {23254--23273},
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/wang22ai/wang22ai.pdf},
url = {https://proceedings.mlr.press/v162/wang22ai.html},
abstract = {We study adversarial attacks on linear stochastic bandits: by manipulating the rewards, an adversary aims to control the behaviour of the bandit algorithm. Perhaps surprisingly, we first show that some attack goals can never be achieved. This is in a sharp contrast to context-free stochastic bandits, and is intrinsically due to the correlation among arms in linear stochastic bandits. Motivated by this finding, this paper studies the attackability of a $k$-armed linear bandit environment. We first provide a complete necessity and sufficiency characterization of attackability based on the geometry of the arms’ context vectors. We then propose a two-stage attack method against LinUCB and Robust Phase Elimination. The method first asserts whether the given environment is attackable; and if yes, it poisons the rewards to force the algorithm to pull a target arm linear times using only a sublinear cost. Numerical experiments further validate the effectiveness and cost-efficiency of the proposed attack method.}
}