Adaptive holding for online bottleneck matching with delays

Abstract

Bipartite matching between two sets of objects is widely applied in many applications such as crowdsourcing marketplaces, ride-hailing services and logistics. Depending on the applications, different objectives have been proposed, resulting in different matching problems. Among them, one that is recently proposed is online bottleneck matching with delays (OBM-D), where the objective is to optimize the maximum cost of matches and the cost of a match depends on when the match is formed (i.e., it is delay-aware). Existing solutions for OBM-D usually adopt a holding strategy, which holds the objects involved in a match available for a period so as to reduce the chance that a bad match is formed. Nevertheless, existing holding strategies are all based on human-crafted rules thus cannot adapt to the dynamics of how the objects arrive. In this paper, we propose an adaptive holding strategy which is based on reinforcement learning and develop a method called Adaptive-H on top of the new holding strategy. Besides, we prove theoretical results on how good a randomized algorithm could achieve for the OBM-D problem in terms of competitive ratio. We conduct extensive experiments on both real and synthetic datasets to verify that Adaptive-H outperforms existing algorithms in terms of both effectiveness and efficiency.