Markov Chain Gradient Descent in Hilbert Spaces

TL;DR

This paper introduces a Markov chain-based stochastic gradient algorithm in Hilbert spaces, providing convergence bounds and extending to online regularized learning in reproducing kernel Hilbert spaces with Markovian samples.

Contribution

It develops convergence analysis for Markov chain gradient descent in Hilbert spaces and extends results to online kernel learning with Markovian data.

Findings

Probabilistic upper bounds on convergence.

Extension to online regularized learning in RKHS.

Analysis applicable to Markovian data streams.

Abstract

In this paper, we study a Markov chain-based stochastic gradient algorithm in general Hilbert spaces, aiming at approximating the optimal solution of a quadratic loss function. We establish probabilistic upper bounds on its convergence. We further extend these results to an online regularized learning algorithm in reproducing kernel Hilbert spaces, where the samples are drawn along a Markov chain trajectory.