Learning Neural Strategy-Proof Matching Mechanism from Examples

Designing two-sided matching mechanisms is challenging when practical demands for matching outcomes are difficult to formalize and the designed mechanism must satisfy theoretical conditions. To address this, prior work has proposed a framework that learns a matching mechanism from examples, using a parameterized family that satisfies properties such as stability. However, despite its usefulness, this framework does not guarantee strategy-proofness (SP), and cannot handle varying numbers of agents or incorporate publicly available contextual information about agents, both of which are crucial in real-world applications. In this paper, we propose a new parametrized family of matching mechanisms that always satisfy strategy-proofness, are applicable for an arbitrary number of agents, and deal with public contextual information of agents, based on the serial dictatorship (SD). This family is represented by NeuralSD, a novel neural network architecture based on SD, where agent rankings in SD are treated as learnable parameters computed from agents' contexts using an attention-based sub-network. To enable learning, we introduce tensor serial dictatorship (TSD), a differentiable relaxation of SD using tensor operations. This allows NeuralSD to be trained end-to-end from example matchings while satisfying SP. We conducted experiments to learn a matching mechanism from matching examples while satisfying SP. We demonstrated that our method outperformed baselines in predicting matchings and on several metrics for goodness of matching outcomes.