Global convergence of gradient descent for phase retrieval

TL;DR

This paper proves that gradient descent almost always converges to a global minimum in phase retrieval problems by establishing a tensor-based criterion for benign landscapes and bounded gradient trajectories.

Contribution

It introduces a tensor-based criterion for benign landscapes in phase retrieval and proves convergence of gradient descent from almost all initial points.

Findings

Gradient descent converges to a global minimum in phase retrieval.

A tensor-based criterion for benign landscape is established.

Gradient trajectories are shown to be bounded.

Abstract

We propose a tensor-based criterion for benign landscape in phase retrieval and establish boundedness of gradient trajectories. This implies that gradient descent will converge to a global minimum for almost every initial point.