Decentralized, Communication- and Coordination-free Learning in Structured Matching Markets
This addresses the challenge of decentralized learning in competitive matching markets for agents who need to learn preferences while competing, though it appears to be an incremental improvement over prior work on structured markets.
The paper tackles the problem of online learning in competitive two-sided matching markets where agents must learn preferences over firms through repeated interactions while competing for matches. The authors propose decentralized algorithms that require no communication or coordination between agents and achieve logarithmic regret growth under realistic structural assumptions on preferences.
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. Our results show that, in the case of matching markets, competition need not drastically affect the performance of decentralized, communication and coordination free online learning algorithms.