Robust Decentralized Multi-armed Bandits: From Corruption-Resilience to Byzantine-Resilience

Decentralized cooperative multi-agent multi-armed bandits (DeCMA2B) considers how multiple agents collaborate in a decentralized multi-armed bandit setting. Though this problem has been extensively studied in previous work, most existing methods remain susceptible to various adversarial attacks. In this paper, we first study DeCMA2B with adversarial corruption, where an adversary can corrupt reward observations of all agents with a limited corruption budget. We propose a robust algorithm, called DeMABAR, which ensures that each agent's individual regret suffers only an additive term proportional to the corruption budget. Then we consider a more realistic scenario where the adversary can only attack a small number of agents. Our theoretical analysis shows that the DeMABAR algorithm can also almost completely eliminate the influence of adversarial attacks and is inherently robust in the Byzantine setting, where an unknown fraction of the agents can be Byzantine, i.e., may arbitrarily select arms and communicate wrong information. We also conduct numerical experiments to illustrate the robustness and effectiveness of the proposed method.

A Near-optimal, Scalable and Corruption-tolerant Framework for Stochastic Bandits: From Single-Agent to Multi-Agent and Beyond

We investigate various stochastic bandit problems in the presence of adversarial corruption. A seminal contribution to this area is the BARBAR~\citep{gupta2019better} algorithm, which is both simple and efficient, tolerating significant levels of corruption with nearly no degradation in performance. However, its regret upper bound exhibits a complexity of $O(KC)$, while the lower bound is $\Omega(C)$. In this paper, we enhance the BARBAR algorithm by proposing a novel framework called BARBAT, which eliminates the factor of $K$ and achieves an optimal regret bound up to a logarithmic factor. We also demonstrate how BARBAT can be extended to various settings, including graph bandits, combinatorial semi-bandits, batched bandits and multi-agent bandits. In comparison to the Follow-The-Regularized-Leader (FTRL) family of methods, which provide a best-of-both-worlds guarantee, our approach is more efficient and parallelizable. Notably, FTRL-based methods face challenges in scaling to batched and multi-agent settings.