Fair Multi-Agent Bandits

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 $O\left(N³ \log \frac{B}{\Delta} f(\log T) \log T \right)$ (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 $\log T$.