In this paper, we investigate the learnability of the function approximator that approximates Nash equilibrium (NE) for games generated from a distribution. First, we offer a generalization bound using the Probably Approximately Correct (PAC) learning model. The bound describes the gap between the expected loss and empirical loss of the NE approximator. Afterward, we prove the agnostic PAC learnability of the Nash approximator. In addition to theoretical analysis, we demonstrate an application of NE approximator in experiments. The trained NE approximator can be used to warm-start and accelerate classical NE solvers. Together, our results show the practicability of approximating NE through function approximation.

翻译：本文研究了从某分布生成的博弈中，用于近似纳什均衡（NE）的函数逼近器的可学习性。首先，我们利用概率近似正确（PAC）学习模型给出了一个泛化界。该界描述了NE逼近器的期望损失与经验损失之间的差距。随后，我们证明了纳什逼近器在不可知PAC框架下的可学习性。除理论分析外，我们还通过实验展示了NE逼近器的应用。训练后的NE逼近器可用于预热启动并加速经典NE求解器。综合而言，我们的结果表明，通过函数逼近近似NE具有实践可行性。