Beyond $\log^2(T)$ Regret for Decentralized Bandits in Matching Markets

TL;DR

This paper introduces decentralized algorithms for regret minimization in two-sided matching markets with bandit feedback, achieving near-optimal regret bounds and improving upon previous methods, especially in complex market settings.

Contribution

The paper presents new decentralized algorithms that reduce regret to near-logarithmic levels in general markets and achieve optimal regret in markets with stability conditions, surpassing prior work.

Findings

Achieved $O( ext{log}^{1+ ext{ε}}(T))$ regret for general markets.

Established $ ext{Θ}( ext{log}(T))$ regret in markets with stability.

Demonstrated algorithm superiority through simulations.

Abstract

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, 2020b, Sankararaman et al. 2020). 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 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 serial dictatorship setting, when all arms have the same preference over the agents. We propose a phase-based algorithm, wherein each phase, besides deleting the globally communicated dominated arms the agents locally delete arms with which they collide often. This local deletion is pivotal in breaking deadlocks arising from rank heterogeneity of agents across arms. We further demonstrate the superiority of our algorithm over existing works through simulations.