Equilibrium in classification: a new game theoretic approach to supervised learning.

A new Framework based on Optimization and Game Theory (FROG) for the supervised classification problem is proposed. The problem is converted into a normal form game in which players are instances of the data that have to choose their class in order to maximize a payoff computed based on the F1 score. The Nash equilibrium of the game represents the correct classification and can be computed as the optimum of a real-valued function. This function is used to estimate the parameters of a classification model such that the resulting probabilities correspond or at least approximate the game equilibrium. CMA-ES is used to minimize this function. Numerical experiments are used to illustrate the potential of this approach.