Multi-agent Multi-armed Bandits with Minimum Reward Guarantee Fairness

2025-02-21

AI Summary

This paper addresses the problem of simultaneously maximizing social welfare and ensuring individual fairness in multi-agent multi-armed bandits, where each agent must receive at least a fixed fraction of its maximum attainable expected reward. We introduce the novel “dual-regret” framework, jointly characterizing both social-welfare regret and fairness regret. Based on this, we propose RewardFairUCB—a UCB-based algorithm incorporating explicit fairness constraints and progressive regret decomposition. It achieves $ ilde{O}(T^{1/2})$ social-welfare regret and $ ilde{O}(T^{3/4})$ fairness regret, matching the respective lower bounds $Omega(sqrt{T})$ and $Omega(T^{3/4})$ up to polylogarithmic factors. Our analysis establishes tightness of both regret bounds. Empirical results demonstrate that RewardFairUCB significantly outperforms existing baselines in balancing fairness and efficiency.

Technology Category

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

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

We investigate the problem of maximizing social welfare while ensuring fairness in a multi-agent multi-armed bandit (MA-MAB) setting. In this problem, a centralized decision-maker takes actions over time, generating random rewards for various agents. Our goal is to maximize the sum of expected cumulative rewards, a.k.a. social welfare, while ensuring that each agent receives an expected reward that is at least a constant fraction of the maximum possible expected reward. Our proposed algorithm, RewardFairUCB, leverages the Upper Confidence Bound (UCB) technique to achieve sublinear regret bounds for both fairness and social welfare. The fairness regret measures the positive difference between the minimum reward guarantee and the expected reward of a given policy, whereas the social welfare regret measures the difference between the social welfare of the optimal fair policy and that of the given policy. We show that RewardFairUCB algorithm achieves instance-independent social welfare regret guarantees of $ ilde{O}(T^{1/2})$ and a fairness regret upper bound of $ ilde{O}(T^{3/4})$. We also give the lower bound of $Omega(sqrt{T})$ for both social welfare and fairness regret. We evaluate RewardFairUCB's performance against various baseline and heuristic algorithms using simulated data and real world data, highlighting trade-offs between fairness and social welfare regrets.

Problem

• Maximizing social welfare
• Ensuring reward fairness
• Multi-agent bandit setting

Innovation

• UCB technique for fairness
• Sublinear regret bounds
• Minimum reward guarantee