Bandit Learning in Decentralized Matching Markets
This addresses the challenge of learning in competitive, decentralized environments for applications like online markets or resource allocation, representing an incremental extension of bandit methods to multi-player settings.
The paper tackles the problem of decentralized matching markets where players must learn preferences without prior knowledge or communication, extending the multi-armed bandit framework to a competitive, multi-player setting. It introduces an algorithm achieving O(log(T)) stable regret with shared arm preferences and O(log(T)^2) regret with no preference assumptions, and shows incentive compatibility under shared preferences.
We study two-sided matching markets in which one side of the market (the players) does not have a priori knowledge about its preferences for the other side (the arms) and is required to learn its preferences from experience. Also, we assume the players have no direct means of communication. This model extends the standard stochastic multi-armed bandit framework to a decentralized multiple player setting with competition. We introduce a new algorithm for this setting that, over a time horizon $T$, attains $\mathcal{O}(\log(T))$ stable regret when preferences of the arms over players are shared, and $\mathcal{O}(\log(T)^2)$ regret when there are no assumptions on the preferences on either side. Moreover, in the setting where a single player may deviate, we show that the algorithm is incentive compatible whenever the arms' preferences are shared, but not necessarily so when preferences are fully general.