Multi-Agent Stochastic Bandits Robust to Adversarial Corruptions

TL;DR

This paper introduces a robust multi-agent bandit algorithm resilient to adversarial reward corruptions, achieving near-optimal regret bounds and improving existing results in both single-agent and multi-agent settings.

Contribution

The authors propose a novel cooperative learning algorithm that maintains low regret despite adversarial corruptions, with theoretical guarantees on its robustness and performance.

Findings

Regret increases additively with corruption budget C.

Algorithm outperforms previous methods in heterogeneous multi-agent scenarios.

Improves regret bounds in single-agent and homogeneous multi-agent cases.

Abstract

We study the problem of multi-agent multi-armed bandits with adversarial corruption in a heterogeneous setting, where each agent accesses a subset of arms. The adversary can corrupt the reward observations for all agents. Agents share these corrupted rewards with each other, and the objective is to maximize the cumulative total reward of all agents (and not be misled by the adversary). We propose a multi-agent cooperative learning algorithm that is robust to adversarial corruptions. For this newly devised algorithm, we demonstrate that an adversary with an unknown corruption budget $C$ only incurs an additive $O((L / L_{\min}) C)$ term to the standard regret of the model in non-corruption settings, where $L$ is the total number of agents, and $L_{\min}$ is the minimum number of agents with mutual access to an arm. As a side-product, our algorithm also improves the state-of-the-art regret bounds when reducing to both the single-agent and homogeneous multi-agent scenarios, tightening multiplicative $K$ (the number of arms) and $L$ (the number of agents) factors, respectively.