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.

翻译：我们研究了高斯相位恢复问题中的加速优化方法。在此设定下，我们证明了采用Polyak或Nesterov动量的梯度方法与梯度下降法具有相似的隐式正则化效应。这种隐式正则化确保算法始终处于一个良好的区域——在该区域中，尽管代价函数整体上非凸，但其具有强凸性和光滑性。这保证了这些加速方法比梯度下降法达到更快的收敛速度。实验证据表明，在实际应用中加速方法的收敛速度确实优于梯度下降法。