We investigate various stochastic bandit problems in the presence of adversarial corruptions. A seminal work for this problem is the BARBAR~\cite{gupta2019better} algorithm, which achieves both robustness and efficiency. However, it suffers from a regret of $O(KC)$, which does not match the lower bound of $Ω(C)$, where $K$ denotes the number of arms and $C$ denotes the corruption level. In this paper, we first improve the BARBAR algorithm by proposing a novel framework called BARBAT, which eliminates the factor of $K$ to achieve an optimal regret bound up to a logarithmic factor. We also extend BARBAT to various settings, including multi-agent bandits, graph bandits, combinatorial semi-bandits and batched bandits. Compared with the Follow-the-Regularized-Leader framework, our methods are more amenable to parallelization, making them suitable for multi-agent and batched bandit settings, and they incur lower computational costs, particularly in semi-bandit problems. Numerical experiments verify the efficiency of the proposed methods.

翻译：本文研究了存在对抗性扰动情况下的多种随机赌博机问题。该领域的奠基性工作是BARBAR算法，它同时实现了鲁棒性和高效性。然而，该算法的遗憾界为$O(KC)$，未能达到下界$Ω(C)$，其中$K$表示臂的数量，$C$表示扰动水平。本文首先通过提出名为BARBAT的新型框架改进了BARBAR算法，该框架消除了$K$因子，从而实现了对数因子内的最优遗憾界。我们还将BARBAT扩展到多种场景，包括多智能体赌博机、图赌博机、组合半赌博机和批处理赌博机。与跟随正则化领导者框架相比，我们的方法更易于并行化，适用于多智能体和批处理赌博机场景，并且计算成本更低，尤其在半赌博机问题中。数值实验验证了所提方法的有效性。