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

In this paper, we shed new light on the generalization ability of deep learning-based solvers for Traveling Salesman Problems (TSP). Specifically, we introduce a two-player zero-sum framework between a trainable \emph{Solver} and a \emph{Data Generator}, where the Solver aims to solve the task instances provided by the Generator, and the Generator aims to generate increasingly difficult instances for improving the Solver. Grounded in \textsl{Policy Space Response Oracle} (PSRO) methods, our two-player framework outputs a population of best-responding Solvers, over which we can mix and output a combined model that achieves the least exploitability against the Generator, and thereby the most generalizable performance on different TSP tasks. We conduct experiments on a variety of TSP instances with different types and sizes. Results suggest that our Solvers achieve the state-of-the-art performance even on tasks the Solver never meets, whilst the performance of other deep learning-based Solvers drops sharply due to over-fitting. On real-world instances from \textsc{TSPLib}, our method also attains a \textbf{12\%} improvement, in terms of optimal gap, over the best baseline model. To demonstrate the principle of our framework, we study the learning outcome of the proposed two-player game and demonstrate that the exploitability of the Solver population decreases during training, and it eventually approximates the Nash equilibrium along with the Generator.