Constant Regret Primal-Dual Policy for Multiway Dynamic Matching

We study a discrete-time dynamic multiway matching model. There are finitely many agent types that arrive stochastically and wait to be matched. State-of-the-art dynamic matching policies in the literature require the knowledge of all system parameters to determine an optimal basis of the fluid relaxation, and focus on controlling the number of waiting agents using only matches within the optimal basis. In this paper, we propose a primal-dual policy that schedules matches for future arrivals based on an estimator for the dual solution. Our policy does not require the knowledge of the arrival rates and operates with greater flexibility as it does not restrict matches to only the match types within an optimal basis. We show that our policy is the first to achieve constant regret at all times under unknown arrival rates, and when the arrival rates are known, it achieves the optimal scaling. Furthermore, when the arrival rates are known, the primal-dual policy significantly outperforms alternative dynamic matching policies in several numerical simulations. This paper was accepted by Baris Ata, stochastic models and simulation. Funding: J. Xu is supported in part by the National Science Foundation [Grant CCF-1856424 and NSF CAREER award CCF-2144593]. S. H. Yu is supported in part by the National Science Foundation [Grant CCF-1856424]. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2023.01668 .