Convergence and consistency of ERM algorithm with uniformly ergodic Markov chain samples

Abstract

This paper studies the convergence rate and consistency of Empirical Risk Minimization algorithm, where the samples need not be independent and identically distributed (i.i.d.) but can come from uniformly ergodic Markov chain (u.e.M.c.). We firstly establish the generalization bounds of Empirical Risk Minimization algorithm with u.e.M.c. samples. Then we deduce that the Empirical Risk Minimization algorithm on the base of u.e.M.c. samples is consistent and owns a fast convergence rate.