Feature Based Dynamic Matching

Abstract

Motivated by matching platforms that match agents in a centralized manner, we study dynamic two-sided matching in a setting where both customers (demand) and service providers (supply) are heterogeneous and the pool of service providers is limited. We model heterogeneity on the two sides of the market by i.i.d demand weight vectors and i.i.d supply feature vectors, with possibly different distributions. The matching of a demand-supply pair generates a utility that depends on their weight and feature vectors. We adopt a notion of regret, specifically the additive loss relative to the utility (per match) achievable in the continuum limit $(n \to \infty)$, as our performance metric for matching policies. Simple myopic policies suffer non-vanishing $\Omega(1)$ regret in large markets. We propose a forward-looking supply-aware policy dubbed Simulate-Optimize-Assign-Repeat (SOAR) which balances between producing high match utility for the current customer and preserving valuable supply for future customers. We prove that \textsf{SOAR} achieves the optimal regret scaling under different assumptions on the demand and supply distributions. En-route to proving our guarantees we develop a novel framework for analysing the performance of our SOAR policy which may be of wider applicability and independent interest. As a corollary of our techniques, we also resolve an open problem posed in Kanoria 2022.

Keywords: matching markets, dynamic matching, simulation based policies, regret analysis