A Linear Matching Bandit Approach to Online Multi-Human Multi-Robot Teaming

2026-06-28

AI Summary

This work addresses the dynamic matching problem in online multi-human multi-robot teaming where robot characteristics are initially unknown. The authors propose LinMatch, an online learning algorithm grounded in the linear matching bandit framework. At each round, LinMatch models the matching process as a maximum-weight matching problem formulated via linear programming, leveraging confidence interval estimation and an optimistic matching strategy, and efficiently solves it using the Hungarian algorithm. Theoretical analysis establishes, for the first time, tight upper and lower bounds for linear-feature-based matching, proving that LinMatch achieves the optimal regret bound of $\tilde{\Theta}(d\sqrt{MKT})$, where $T$ is the time horizon, $d$ the feature dimensionality, $M$ the number of humans, and $K$ the number of robots. This result confirms both the theoretical optimality and broad applicability of LinMatch in multi-agent dynamic matching tasks.

Abstract

We address the problem of online multi-human multi-robot teaming through the lens of a linear matching bandit framework, where a learner assigns robots with unknown features from a fixed pool to distinct sets of human agents over multiple rounds. To solve this problem, we propose LinMatch, an online learning algorithm that updates the confidence intervals of the unknown features and makes the optimistic matching under uncertainty. The contributions and novelty of this work are twofold. First, we recast the optimistic matching problem in each round as a linear program of maximum weighted matching, efficiently solvable by the celebrated Hungarian algorithm. Second, we provide novel bounds for matching with linear feature problems, showing an upper bound of $\tilde{O}(d\sqrt{MKT})$ and a minimax lower bound of $Ω(d\sqrt{MKT})$, establishing a tight optimal regret rate of $\tildeΘ(d\sqrt{MKT})$. This demonstrates that LinMatch achieves strictly optimal achievable regret with respect to the total number of rounds $T$, the feature dimension $d$, and the matching parameters $M$ and $K$. The proposed algorithm and bounds apply to a wide range of matching problems with applications beyond human-robot matching, such as housing allocation, recommendation systems, and more.

Problem

• online multi-human multi-robot teaming
• linear matching bandit
• unknown robot features
• dynamic team formation
• matching under uncertainty

Innovation

• linear matching bandit
• online learning
• maximum weighted matching
• regret bound
• Hungarian algorithm