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

23 September 2022
Matthew D. Jones
Huy Le Nguyen
Thy Nguyen
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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 TTT. We propose a new efficient algorithm with lower regret than even previous inefficient ones. For NNN agents, KKK arms, and TTT rounds, our approach has a regret bound of O~(NKT+NK)\tilde{O}(\sqrt{NKT} + NK)O~(NKT​+NK). This is an improvement to the previous approach, which has regret bound of O~(min⁡(NK,NK3/2)T)\tilde{O}( \min(NK, \sqrt{N} K^{3/2})\sqrt{T})O~(min(NK,N​K3/2)T​). We also complement our efficient algorithm with an inefficient approach with O~(KT+N2K)\tilde{O}(\sqrt{KT} + N^2K)O~(KT​+N2K) regret. The experimental findings confirm the effectiveness of our efficient algorithm compared to the previous approaches.

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