Stochastic Fixed Point Optimization Algorithm for Classifier Ensemble

This paper considers a classifier ensemble problem with sparsity and diversity learning, which arises in the field of machine learning, and shows that the classifier ensemble problem can be formulated as a convex stochastic optimization problem over the fixed point set of a quasi-nonexpansive mapping. Specifically, for such a problem, this paper proposes an algorithm referred to as the stochastic fixed point optimization algorithm and performs a convergence analysis for three types of step size: 1) constant step size; 2) decreasing step size; and 3) a step size computed by line searches. In the case of a constant step size, the results indicate that a sufficiently small constant step size allows a solution to the problem to be approximated. In the case of a decreasing step size, conditions are shown under which the algorithm converges in probability to a solution. For the third case, a variation of the basic proposed algorithm also achieves convergence in probability to a solution. The high classification accuracies of the proposed algorithms are demonstrated through numerical comparisons with the conventional algorithm.