Doubly Adversarial Federated Bandits

TL;DR

This paper introduces a new federated multi-armed bandit problem with a doubly adversarial setting, providing theoretical regret bounds and a near-optimal algorithm that operates without sharing detailed feedback among agents.

Contribution

It formulates the doubly adversarial federated bandit problem, derives regret lower bounds, and proposes FEDEXP3, a near-optimal algorithm that works with limited communication.

Findings

FEDEXP3 achieves sub-linear regret in the bandit feedback setting.

Theoretical regret bounds are established for various feedback scenarios.

Numerical experiments validate the effectiveness of FEDEXP3 on synthetic and real data.

Abstract

We study a new non-stochastic federated multi-armed bandit problem with multiple agents collaborating via a communication network. The losses of the arms are assigned by an oblivious adversary that specifies the loss of each arm not only for each time step but also for each agent, which we call ``doubly adversarial". In this setting, different agents may choose the same arm in the same time step but observe different feedback. The goal of each agent is to find a globally best arm in hindsight that has the lowest cumulative loss averaged over all agents, which necessities the communication among agents. We provide regret lower bounds for any federated bandit algorithm under different settings, when agents have access to full-information feedback, or the bandit feedback. For the bandit feedback setting, we propose a near-optimal federated bandit algorithm called FEDEXP3. Our algorithm gives a positive answer to an open question proposed in Cesa-Bianchi et al. (2016): FEDEXP3 can guarantee a sub-linear regret without exchanging sequences of selected arm identities or loss sequences among agents. We also provide numerical evaluations of our algorithm to validate our theoretical results and demonstrate its effectiveness on synthetic and real-world datasets