Generalization Performance of ERM Algorithm with Geometrically Ergodic Markov Chain Samples

The previous works describing the generalization ability of learning algorithms are based on independent and identically distributed (i.i.d.) samples. In this paper we go far beyond this classical framework by studying the learning performance of the empirical risk minimization (ERM) algorithm with Markov chain samples. We obtain the bound on the rate of uniform convergence of the ERM algorithm with geometrically ergodic Markov chain samples, as an application of our main result we establish the bounds on the generalization performance of the ERM algorithm, and show that the ERM algorithm with geometrically ergodic Markov chain samples is consistent. These results obtained in this paper extend the previously known results of i.i.d. observations to the case of Markov dependent samples.