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Beyond $log^2(T)$ regret for decentralized bandits in matching markets
Soumya Basu · Karthik Abinav Sankararaman · Abishek Sankararaman

Wed Jul 21 07:35 PM -- 07:40 PM (PDT) @ None
We design decentralized algorithms for regret minimization in the two sided matching market with one-sided bandit feedback that significantly improves upon the prior works (Liu et al.\,2020a, Sankararaman et al.\,2020, Liu et al.\,2020b). First, for general markets, for any $\varepsilon > 0$, we design an algorithm that achieves a $O(\log^{1+\varepsilon}(T))$ regret to the agent-optimal stable matching, with unknown time horizon $T$, improving upon the $O(\log^{2}(T))$ regret achieved in (Liu et al.\,2020b). Second, we provide the optimal $\Theta(\log(T))$ agent-optimal regret for markets satisfying {\em uniqueness consistency} -- markets where leaving participants don't alter the original stable matching. Previously, $\Theta(\log(T))$ regret was achievable (Sankararaman et al.\,2020, Liu et al.\,2020b) in the much restricted {\em serial dictatorship} setting, when all arms have the same preference over the agents. We propose a phase based algorithm, where in each phase, besides deleting the globally communicated dominated arms the agents locally delete arms with which they collide often. This \emph{local deletion} is pivotal in breaking deadlocks arising from rank heterogeneity of agents across arms. We further demonstrate superiority of our algorithm over existing works through simulations.

Author Information

Soumya Basu (Google)
Karthik Abinav Sankararaman (Facebook)
Abishek Sankararaman (Amazon Web Services)

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