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arXiv · 1809.04216

On Markov Chain Gradient Descent

Tao Sun·Yuejiao Sun·Wotao Yin
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Abstract

Stochastic gradient methods are the workhorse (algorithms) of large-scale optimization problems in machine learning, signal processing, and other computational sciences and engineering. This paper studies Markov chain gradient descent, a variant of stochastic gradient descent where the random samples are taken on the trajectory of a Markov chain. Existing results of this method assume convex objectives and a reversible Markov chain and thus have their limitations. We establish new non-ergodic convergence under wider step sizes, for nonconvex problems, and for non-reversible finite-state Markov chains. Nonconvexity makes our method applicable to broader problem classes. Non-reversible finite-state Markov chains, on the other hand, can mix substatially faster. To obtain these results, we introduce a new technique that varies the mixing levels of the Markov chains. The reported numerical results validate our contributions.

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Tao Sun, Yuejiao Sun, Wotao Yin. 2018-09-12. On Markov Chain Gradient Descent. https://arxiv.org/abs/1809.04216

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