  We initiate the study of deep learning for the automated design of two-sided
matching mechanisms. What is of most interest is to use machine learning to
understand the possibility of new tradeoffs between strategy-proofness and
stability. These properties cannot be achieved simultaneously, but the
efficient frontier is not understood. We introduce novel differentiable
surrogates for quantifying ordinal strategy-proofness and stability and use
them to train differentiable matching mechanisms that map discrete preferences
to valid randomized matchings. We demonstrate that the efficient frontier
characterized by these learned mechanisms is substantially better than that
achievable through a convex combination of baselines of deferred acceptance
(stable and strategy-proof for only one side of the market), top trading cycles
(strategy-proof for one side, but not stable), and randomized serial
dictatorship (strategy-proof for both sides, but not stable). This gives a new
target for economic theory and opens up new possibilities for machine learning
pipelines in matching market design.
