Optimizing Relevance and Diversity in Online Matching Markets: A Time-Adaptive Attenuation Approach

Real-world online matching markets (OMMs) often involve multiple objectives, such as maximizing relevance and diversity in online recommendation and crowdsourcing systems. In this paper, we propose a generic bi-objective maximization model for OMMs with the following features: (1) there are two types of agents—offline and online—with online agents arriving dynamically and stochastically; (2) upon each online agent’s arrival, an immediate and irrevocable decision must be made regarding which subset of relevant offline agents to assign; and (3) each offline and online agent has a specific matching capacity, i.e., an upper bound on the number of allowable matchings. Our model supports two general linear objective functions defined over all possible assignments to online agents. We formulate a bi-objective linear program (LP) and design an LP-based parameterized algorithm. Departing from prevalent non-adaptive attenuation methods, we introduce a time-adaptive attenuation framework that achieves an almost tight competitive ratio for each objective. To complement our theoretical analysis, we implement the proposed algorithm and evaluate it against several heuristics using two real-world datasets. Extensive experimental results demonstrate the flexibility and effectiveness of our approach, validating our theoretical predictions.