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

2020-03-05 | |  68 |   48 |   0

Abstract

Stochastic gradient descent (SGD) on a low-rank factorization (Burer & Monteiro, 2003) 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 图片.png 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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