Randomized coordinate gradient descent almost surely escapes strict saddle points

Ziang Chen; Yingzhou Li; Zihao Li

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arXiv · 2508.07535

Randomized coordinate gradient descent almost surely escapes strict saddle points

Ziang Chen·Yingzhou Li·Zihao Li

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Abstract

We analyze the behavior of randomized coordinate gradient descent for nonconvex optimization, proving that under standard assumptions, the iterates almost surely escape strict saddle points. By formulating the method as a nonlinear random dynamical system and characterizing neighborhoods of critical points, we establish this result through the center-stable manifold theorem.

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Ziang Chen, Yingzhou Li, Zihao Li. 2025-08-11. Randomized coordinate gradient descent almost surely escapes strict saddle points. https://arxiv.org/abs/2508.07535

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