An Efficient Algorithm for Fair Multi-Agent Multi-Armed Bandit with Low Regret

TL;DR

This paper introduces a new efficient multi-agent multi-armed bandit algorithm that optimizes fairness via Nash social welfare with significantly lower regret, outperforming previous methods both theoretically and experimentally.

Contribution

The paper presents a novel efficient algorithm for fair multi-agent bandits with improved regret bounds, advancing the state-of-the-art in fairness-aware online learning.

Findings

The efficient algorithm achieves a regret of (\u221a{NKT} + NK)

Experimental results show the new algorithm outperforms previous approaches

The paper also provides a less efficient method with different regret bounds.

Abstract

Recently a multi-agent variant of the classical multi-armed bandit was proposed to tackle fairness issues in online learning. Inspired by a long line of work in social choice and economics, the goal is to optimize the Nash social welfare instead of the total utility. Unfortunately previous algorithms either are not efficient or achieve sub-optimal regret in terms of the number of rounds $T$. We propose a new efficient algorithm with lower regret than even previous inefficient ones. For $N$ agents, $K$ arms, and $T$ rounds, our approach has a regret bound of $\tilde{O}(\sqrt{NKT} + NK)$. This is an improvement to the previous approach, which has regret bound of $\tilde{O}( \min(NK, \sqrt{N} K^{3/2})\sqrt{T})$. We also complement our efficient algorithm with an inefficient approach with $\tilde{O}(\sqrt{KT} + N^2K)$ regret. The experimental findings confirm the effectiveness of our efficient algorithm compared to the previous approaches.