  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.
