mlsanityData to 14 Oct 2026

Acceleration and Implicit Regularization in Gaussian Phase Retrieval

arXiv 2311.12888 ↗First posted 21 Nov 2023math.OC cs.LG math.STcited by 1

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Abstract (arXiv)

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.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 29 of its 62 references that are in the map. First posted on arXiv 21 Nov 2023.

Builds on

29 of 62 references.

References · 29

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  2. 2017Implicit Regularization in Matrix Factorizationcited by 322
  3. 2020Kernel and Rich Regimes in Overparametrized Modelscited by 306
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  5. 2016A Geometric Analysis of Phase Retrievalcited by 92
  6. 2019Implicit Regularization for Optimal Sparse Recoverycited by 80
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  11. 2023Implicit regularization in Heavy-ball momentum accelerated stochastic gradient descentcited by 25
  12. 2017Solving (most) of a set of quadratic equalities: Composite optimization for robust phase retrievalcited by 24
17 more
  1. 2013Exact and Stable Covariance Estimation from Quadratic Sampling via Convex Programmingcited by 20
  2. 2019Implicit Regularization of Accelerated Methods in Hilbert Spacescited by 14
  3. 2018Nonconvex Matrix Factorization from Rank-One Measurementscited by 13
  4. 2020Recursive Importance Sketching for Rank Constrained Least Squares: Algorithms and High-order Convergencecited by 11
  5. 2022Randomly Initialized Alternating Least Squares: Fast Convergence for Matrix Sensingcited by 11
  6. 2022Practical Phase Retrieval Using Double Deep Image Priorscited by 10
  7. 2020A Continuous-Time Mirror Descent Approach to Sparse Phase Retrievalcited by 9
  8. 2020Fast Global Convergence for Low-rank Matrix Recovery via Riemannian Gradient Descent with Random Initializationcited by 9
  9. 2016Sparse Phase Retrieval via Truncated Amplitude Flowcited by 8
  10. 2015The local convexity of solving systems of quadratic equationscited by 6
  11. 2020Hadamard Wirtinger Flow for Sparse Phase Retrievalcited by 6
  12. 2018Accelerated Wirtinger Flow: A fast algorithm for ptychographycited by 5
  13. 2020Quickly Finding a Benign Region via Heavy Ball Momentum in Non-Convex Optimizationcited by 5
  14. 2022Bures-Wasserstein Barycenters and Low-Rank Matrix Recoverycited by 5
  15. 2018Analytical Convergence Regions of Accelerated Gradient Descent in Nonconvex Optimization under Regularity Conditioncited by 3
  16. 2019Holographic Phase Retrieval and Reference Designcited by 3
  17. 2021Towards Low-Photon Nanoscale Imaging: Holographic Phase Retrieval via Maximum Likelihood Optimizationcited by 3

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  1. 2025A Smoothing Newton Method for Rank-one Matrix Recoverycited by 0