Competing Bandits in Time Varying Matching Markets

TL;DR

This paper introduces a method for online learning in non-stationary two-sided matching markets with time-varying preferences, achieving near-optimal regret bounds despite changing preferences.

Contribution

It proposes a versatile algorithm that handles any preference structure and variation scenario, extending prior fixed-preference models to dynamic settings.

Findings

Achieves sub-linear regret of (L_T^{1/2} T^{1/2}) with known preference changes.

Matches optimal single-agent learning rates despite market competition.

Extends to scenarios with unknown number of preference changes.

Abstract

We study the problem of online learning in two-sided non-stationary matching markets, where the objective is to converge to a stable match. In particular, we consider the setting where one side of the market, the arms, has fixed known set of preferences over the other side, the players. While this problem has been studied when the players have fixed but unknown preferences, in this work we study the problem of how to learn when the preferences of the players are time varying and unknown. Our contribution is a methodology that can handle any type of preference structure and variation scenario. We show that, with the proposed algorithm, each player receives a uniform sub-linear regret of {$\widetilde{\mathcal{O}}(L^{1/2}_TT^{1/2})$} up to the number of changes in the underlying preferences of the agents, $L_T$. Therefore, we show that the optimal rates for single-agent learning can be achieved in spite of the competition up to a difference of a constant factor. We also discuss extensions of this algorithm to the case where the number of changes need not be known a priori.