MAGNOLIA: Matching Algorithms via GNNs for Online Value-to-go Approximation
Alexandre Hayderi, Amin Saberi, Ellen Vitercik, Anders Wikum
TL;DR
The paper tackles online Bayesian bipartite matching (OBBM), where irrevocable online decisions must maximize a final weighted matching under uncertain future arrivals. It introduces Magnolia, a Graph Neural Network that learns to approximate the value-to-go (VTG) of each action, effectively emulating the online optimal policy OPT_on through VTG predictions. Theoretical results show VTG can be locally approximated on bipartite random geometric graphs via small, locally aggregating subgraphs, providing justification for GNN-based VTG estimation. Empirically, Magnolia outperforms strong baselines across diverse graph families and sizes, demonstrates strong generalization and robustness to noise, and benefits from meta-models to adapt to different regimes, highlighting practical potential for online matching in digital marketplaces.
Abstract
Online Bayesian bipartite matching is a central problem in digital marketplaces and exchanges, including advertising, crowdsourcing, ridesharing, and kidney exchange. We introduce a graph neural network (GNN) approach that emulates the problem's combinatorially-complex optimal online algorithm, which selects actions (e.g., which nodes to match) by computing each action's value-to-go (VTG) -- the expected weight of the final matching if the algorithm takes that action, then acts optimally in the future. We train a GNN to estimate VTG and show empirically that this GNN returns high-weight matchings across a variety of tasks. Moreover, we identify a common family of graph distributions in spatial crowdsourcing applications, such as rideshare, under which VTG can be efficiently approximated by aggregating information within local neighborhoods in the graphs. This structure matches the local behavior of GNNs, providing theoretical justification for our approach.