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In this paper, we introduce a two-player zero-sum framework between atrainable \emph{Solver} and a \emph{Data Generator} to improve thegeneralization ability of deep learning-based solvers for Traveling SalesmanProblem (TSP). Grounded in \textsl{Policy Space Response Oracle} (PSRO)methods, our two-player framework outputs a population of best-respondingSolvers, over which we can mix and output a combined model that achieves theleast exploitability against the Generator, and thereby the most generalizableperformance on different TSP tasks. We conduct experiments on a variety of TSPinstances with different types and sizes. Results suggest that our Solversachieve the state-of-the-art performance even on tasks the Solver never meets,whilst the performance of other deep learning-based Solvers drops sharply dueto over-fitting. To demonstrate the principle of our framework, we study thelearning outcome of the proposed two-player game and demonstrate that theexploitability of the Solver population decreases during training, and iteventually approximates the Nash equilibrium along with the Generator.

A Game-Theoretic Approach for Improving Generalization Ability of TSP Solvers