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arXiv · 1411.1134

Global Convergence of Stochastic Gradient Descent for Some Non-convex Matrix Problems

Christopher De Sa·Kunle Olukotun·Christopher Ré
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Abstract

Stochastic gradient descent (SGD) on a low-rank factorization is commonly employed to speed up matrix problems including matrix completion, subspace tracking, and SDP relaxation. In this paper, we exhibit a step size scheme for SGD on a low-rank least-squares problem, and we prove that, under broad sampling conditions, our method converges globally from a random starting point within $O(ε^{-1} n \log n)$ steps with constant probability for constant-rank problems. Our modification of SGD relates it to stochastic power iteration. We also show experiments to illustrate the runtime and convergence of the algorithm.

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Christopher De Sa, Kunle Olukotun, Christopher Ré. 2015-02-10. Global Convergence of Stochastic Gradient Descent for Some Non-convex Matrix Problems. https://arxiv.org/abs/1411.1134

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