Collaborative Min-Max Regret in Grouped Multi-Armed Bandits

2025-06-12

AI Summary

This paper addresses fair exploration cost sharing across groups in grouped multi-armed bandits by enabling cross-group exploration. We introduce *collaborative regret*—defined as the maximum individual regret over all groups—as the optimization objective. We establish, for the first time, a minimax-minimax modeling framework for collaborative learning and propose Col-UCB, an adaptive algorithm that integrates inter-group observation sharing, dynamic exploration coordination, and structure-aware analysis. Col-UCB achieves near-optimal (up to logarithmic factors) collaborative regret in both minimax and instance-dependent settings. Its theoretical upper bound on collaborative regret is tight, and our analysis reveals that the degree of action-set overlap across groups fundamentally governs the upper limit of collaboration gain. Empirical evaluations demonstrate that Col-UCB significantly outperforms independent learning baselines, with especially pronounced improvements when group action sets exhibit high overlap.

Technology Category

• Machine Learning: Online Learning & Bandits
• Game Theory and Economic Paradigms: Coordination and Collaboration
• Multiagent Systems: Coordination and Collaboration

Application Category

• Economics, Online Markets and Human Computation: The sharing economy
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We study the impact of sharing exploration in multi-armed bandits in a grouped setting where a set of groups have overlapping feasible action sets [Baek and Farias '24]. In this grouped bandit setting, groups share reward observations, and the objective is to minimize the collaborative regret, defined as the maximum regret across groups. This naturally captures applications in which one aims to balance the exploration burden between groups or populations -- it is known that standard algorithms can lead to significantly imbalanced exploration cost between groups. We address this problem by introducing an algorithm Col-UCB that dynamically coordinates exploration across groups. We show that Col-UCB achieves both optimal minimax and instance-dependent collaborative regret up to logarithmic factors. These bounds are adaptive to the structure of shared action sets between groups, providing insights into when collaboration yields significant benefits over each group learning their best action independently.

Problem

• Impact of sharing exploration in grouped multi-armed bandits
• Minimize collaborative regret across overlapping action sets
• Balance exploration burden between groups dynamically

Innovation

• Dynamic exploration coordination across groups
• Optimal minimax and instance-dependent regret
• Adaptive to shared action set structure