Federated Combinatorial Multi-Agent Multi-Armed Bandits

TL;DR

This paper develops a federated learning framework for multi-agent combinatorial bandits that improves regret bounds, reduces communication, and applies to submodular maximization, validated through empirical experiments.

Contribution

It transforms offline approximation algorithms into online multi-agent algorithms with improved regret bounds and communication efficiency, applicable to submodular maximization.

Findings

Achieves sublinear regret growth with respect to time horizon T.

Ensures linear speedup as the number of agents increases.

Requires only a sublinear number of communication rounds.

Abstract

This paper introduces a federated learning framework tailored for online combinatorial optimization with bandit feedback. In this setting, agents select subsets of arms, observe noisy rewards for these subsets without accessing individual arm information, and can cooperate and share information at specific intervals. Our framework transforms any offline resilient single-agent $(\alpha-\epsilon)$-approximation algorithm, having a complexity of $\tilde{\mathcal{O}}(\frac{\psi}{\epsilon^\beta})$, where the logarithm is omitted, for some function $\psi$ and constant $\beta$, into an online multi-agent algorithm with $m$ communicating agents and an $\alpha$-regret of no more than $\tilde{\mathcal{O}}(m^{-\frac{1}{3+\beta}} \psi^\frac{1}{3+\beta} T^\frac{2+\beta}{3+\beta})$. This approach not only eliminates the $\epsilon$ approximation error but also ensures sublinear growth with respect to the time horizon $T$ and demonstrates a linear speedup with an increasing number of communicating agents. Additionally, the algorithm is notably communication-efficient, requiring only a sublinear number of communication rounds, quantified as $\tilde{\mathcal{O}}\left(\psi T^\frac{\beta}{\beta+1}\right)$. Furthermore, the framework has been successfully applied to online stochastic submodular maximization using various offline algorithms, yielding the first results for both single-agent and multi-agent settings and recovering specialized single-agent theoretical guarantees. We empirically validate our approach to a stochastic data summarization problem, illustrating the effectiveness of the proposed framework, even in single-agent scenarios.