  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.
