Multi-Agent Combinatorial-Multi-Armed-Bandit framework for the Submodular Welfare Problem under Bandit Feedback

TL;DR

This paper introduces a multi-agent combinatorial bandit framework for the submodular welfare problem, providing the first regret guarantees under bandit feedback for partition-based utilities with shared constraints.

Contribution

It extends classical submodular welfare algorithms to a multi-agent bandit setting with shared constraints, proposing an explore-then-commit strategy with regret bounds.

Findings

Achieves $ ilde{O}(T^{2/3})$ regret bound.

First regret guarantee for partition-based submodular welfare under bandit feedback.

Framework handles coupled multi-agent allocation constraints.

Abstract

We study the \emph{Submodular Welfare Problem} (SWP), where items are partitioned among agents with monotone submodular utilities to maximize the total welfare under \emph{bandit feedback}. Classical SWP assumes full value-oracle access, achieving $(1-1/e)$ approximations via continuous-greedy algorithms. We extend this to a \emph{multi-agent combinatorial bandit} framework (\textsc{MA-CMAB}), where actions are partitions under full-bandit feedback with non-communicating agents. Unlike prior single-agent or separable multi-agent CMAB models, our setting couples agents through shared allocation constraints. We propose an explore-then-commit strategy with randomized assignments, achieving $\tilde{\mathcal{O}}(T^{2/3})$ regret against a $(1-1/e)$ benchmark, the first such guarantee for partition-based submodular welfare problem under bandit feedback.