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Global convergence of gradient descent for phase retrieval

arXiv 2410.09990 ↗First posted 13 Oct 2024math.OC cs.LGcited by 0

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Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 13 of its 31 references that are in the map. First posted on arXiv 13 Oct 2024.

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13 of 31 references.

References · 13

  1. 2014Phase Retrieval via Wirtinger Flow: Theory and Algorithmscited by 125
  2. 2016A Geometric Analysis of Phase Retrievalcited by 92
  3. 2018Gradient Descent with Random Initialization: Fast Global Convergence for Nonconvex Phase Retrievalcited by 71
  4. 2017Implicit Regularization in Nonconvex Statistical Estimation: Gradient Descent Converges Linearly for Phase Retrieval, Matrix Completion, and Blind Deconvolutioncited by 63
  5. 2013Phase Retrieval using Alternating Minimizationcited by 58
  6. 2015Solving Random Quadratic Systems of Equations Is Nearly as Easy as Solving Linear Systemscited by 50
  7. 2016Solving Systems of Random Quadratic Equations via Truncated Amplitude Flowcited by 29
  8. 2016PhaseMax: Convex Phase Retrieval via Basis Pursuitcited by 25
  9. 2016Phase retrieval with random Gaussian sensing vectors by alternating projectionscited by 15
  10. 2021Solving phase retrieval with random initial guess is nearly as good as by spectral initializationcited by 9
  11. 2023Global convergence of the gradient method for functions definable in o-minimal structurescited by 5
  12. 2021Concentration of Non-Isotropic Random Tensors with Applications to Learning and Empirical Risk Minimizationcited by 4
1 more
  1. 2023The Local Landscape of Phase Retrieval Under Limited Samplescited by 1

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