Stochastic Bandits Robust to Adversarial Attacks

TL;DR

This paper develops robust stochastic bandit algorithms resilient to adversarial reward manipulations, providing tight regret bounds and demonstrating a fundamental difference from corruption models.

Contribution

It introduces new algorithms with proven regret bounds for both known and unknown attack budgets, advancing robustness in adversarial bandit settings.

Findings

Achieves regret bounds of O((K/Δ) log T + KC) and √(KTC) for known attack budgets.

Achieves regret bounds of √(KT) + KC^2 and KC√T for unknown attack budgets.

Provides lower bounds confirming the optimality of the proposed algorithms.

Abstract

This paper investigates stochastic multi-armed bandit algorithms that are robust to adversarial attacks, where an attacker can first observe the learner's action and {then} alter their reward observation. We study two cases of this model, with or without the knowledge of an attack budget $C$, defined as an upper bound of the summation of the difference between the actual and altered rewards. For both cases, we devise two types of algorithms with regret bounds having additive or multiplicative $C$ dependence terms. For the known attack budget case, we prove our algorithms achieve the regret bound of ${O}((K/\Delta)\log T + KC)$ and $\tilde{O}(\sqrt{KTC})$ for the additive and multiplicative $C$ terms, respectively, where $K$ is the number of arms, $T$ is the time horizon, $\Delta$ is the gap between the expected rewards of the optimal arm and the second-best arm, and $\tilde{O}$ hides the logarithmic factors. For the unknown case, we prove our algorithms achieve the regret bound of $\tilde{O}(\sqrt{KT} + KC^2)$ and $\tilde{O}(KC\sqrt{T})$ for the additive and multiplicative $C$ terms, respectively. In addition to these upper bound results, we provide several lower bounds showing the tightness of our bounds and the optimality of our algorithms. These results delineate an intrinsic separation between the bandits with attacks and corruption models [Lykouris et al., 2018].