Acceleration and Implicit Regularization in Gaussian Phase Retrieval
This provides incremental improvements in optimization for a specific nonconvex problem in signal processing and machine learning.
The paper tackles the Gaussian phase retrieval problem by showing that accelerated gradient methods with Polyak or Nesterov momentum achieve faster convergence rates than gradient descent, with experimental evidence confirming this practical speedup.
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.