On the global convergence of randomized coordinate gradient descent for non-convex optimization

Ziang Chen; Yingzhou Li; Jianfeng Lu

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arXiv · 2101.01323

On the global convergence of randomized coordinate gradient descent for non-convex optimization

Ziang Chen·Yingzhou Li·Jianfeng Lu

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Abstract

In this work, we analyze the global convergence property of coordinate gradient descent with random choice of coordinates and stepsizes for non-convex optimization problems. Under generic assumptions, we prove that the algorithm iterate will almost surely escape strict saddle points of the objective function. As a result, the algorithm is guaranteed to converge to local minima if all saddle points are strict. Our proof is based on viewing coordinate descent algorithm as a nonlinear random dynamical system and a quantitative finite block analysis of its linearization around saddle points.

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BibTeX RIS

Ziang Chen, Yingzhou Li, Jianfeng Lu. 2021-01-05. On the global convergence of randomized coordinate gradient descent for non-convex optimization. https://arxiv.org/abs/2101.01323

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