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.

翻译：本文首次探索利用深度学习自动设计双面匹配机制。我们最关注的是通过机器学习理解策略防伪性与稳定性之间达成新权衡的可能性。虽然这两个属性无法同时实现，但其有效前沿尚不明确。我们提出了用于量化序数策略防伪性和稳定性的新型可微代理指标，并利用这些指标训练能够将离散偏好映射到有效随机匹配的可微匹配机制。实验表明，这些学习机制所刻画的有效前沿显著优于通过延迟接受算法（仅对市场单方成立稳定且策略防伪）、顶层交易循环（对单方成立策略防伪但不稳定）和随机序列独裁机制（对双方成立策略防伪但不稳定）等基线方法的凸组合所得结果。这为经济理论提出了新的研究目标，也为匹配市场设计中的机器学习流程开拓了全新可能。