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 {O˜(𝐿1/2𝑇𝑇1/2)} up to the number of changes in the underlying preferences of the agents, 𝐿𝑇. 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.
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Decentralized, communication-and coordination-free learning in structured matching markets
We study the problem of online learning in competitive settings in the context of two-sided matching markets. In particular, one side of the market, the agents, must learn about their preferences over the other side, the firms, through repeated interaction while competing with other agents for successful matches. We propose a class of decentralized, communication- and coordination-free algorithms that agents can use to reach to their stable match in structured matching markets. In contrast to prior works, the proposed algorithms make decisions based solely on an agent’s own history of play and requires no foreknowledge of the firms’ preferences.Our algorithms are constructed by splitting up the statistical problem of learning one’s preferences, from noisy observations, from the problem of competing for firms. We show that under realistic structural assumptions on the underlying preferences of the agents and firms, the proposed algorithms incur a regret which grows at most logarithmically in the time horizon. However, we note that in the worst case, it may grow exponentially in the size of the market.
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- Award ID(s):
- 2125913
- NSF-PAR ID:
- 10434389
- Date Published:
- Journal Name:
- Advances in neural information processing systems
- Volume:
- 35
- ISSN:
- 1049-5258
- Page Range / eLocation ID:
- 15081-92
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
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