Acceleration and Implicit Regularization in Gaussian Phase Retrieval

2023/11/21 by Tyler Maunu, Maunu, Tyler, Martin Molina-Fructuoso +1 · 1 citation
Medicine · Physics and Astronomy · #Advanced X-ray Imaging Techniques #Aortic aneurysm repair treatments #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Optimization and Control (math.OC) #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2311.12888

openalex publication_date 2023/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study accelerated optimization methods in the Gaussian phase retrieval problem. In this setting, we prove that gradient methods with Polyak or Nesterov momentum have similar implicit regularization to gradient descent. This implicit regularization ensures that the algorithms remain in a nice region, where the cost function is strongly convex and smooth despite being nonconvex in general. This ensures that these accelerated methods achieve faster rates of convergence than gradient descent. Experimental evidence demonstrates that the accelerated methods converge faster than gradient descent in practice.

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