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

2026-02-18

AI Summary

This study addresses the problem of submodular welfare maximization among multiple non-communicating agents, each endowed with a monotone submodular utility function, under the constraint that only bandit feedback is available. To tackle this challenge, the authors propose a Multi-Agent Combinatorial Multi-Armed Bandit (MA-CMAB) framework that integrates exploration–exploitation strategies, randomized allocation mechanisms, and submodular optimization techniques to enable efficient decision-making under shared allocation constraints. This work represents the first extension of submodular welfare maximization to a multi-agent bandit setting with shared constraints and establishes the first theoretical regret guarantee in this context: an upper regret bound of Õ(T^{2/3}) relative to a (1−1/e)-approximation benchmark.

Technology Category

• Multiagent Systems: Mechanism Design
• Machine Learning: Online Learning & Bandits
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Responsible Web: Machine-in-the-loop, human agency and autonomy

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.

Problem

• Submodular Welfare Problem
• Multi-Agent Combinatorial Bandits
• Bandit Feedback
• Monotone Submodular Utilities
• Allocation Constraints

Innovation

• Multi-Agent Combinatorial Bandits
• Submodular Welfare Problem
• Bandit Feedback
• Explore-Then-Commit
• Regret Bound