Fair Multi-Agent Bandits

Amir Leshem
6/7/2023
cs.LGcs.CYcs.DC

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Abstract

In this paper, we study the problem of fair multi-agent multi-arm bandit learning when agents do not communicate with each other, except collision information, provided to agents accessing the same arm simultaneously. We provide an algorithm with regret $O\left(N^3 \log \frac{B}Δ f(\log T) \log T \right)$ (assuming bounded rewards, with unknown bound), where $f(t)$ is any function diverging to infinity with $t$. This significantly improves previous results which had the same upper bound on the regret of order $O(f(\log T) \log T )$ but an exponential dependence on the number of agents. The result is attained by using a distributed auction algorithm to learn the sample-optimal matching and a novel order-statistics-based regret analysis. Simulation results present the dependence of the regret on $\log T$.

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Cite this paper

@article{leshem2023fair,
  title  = {Fair Multi-Agent Bandits},
  author = {Amir Leshem},
  year   = {2023},
  eprint = {2306.04498},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2306.04498v2}
}

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