Stochastic algorithms for large-scale composite optimization: the case of likelihood maximization for X-FEL imaging

• 成果类型: Article
• 署名作者: Luke, D. Russell; Schultze, Steffen; Grubmuller, Helmut
• 署名单位: University of Gottingen
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610; 1436-4646
• DOI: 10.1007/s10107-025-02319-9
• 发表日期: 2026-05
• 页码: 407-437
• 关键词: Nonconvex optimization; large-scale optimization; Markov chain; Random function iteration; error bounds; convergence rates; Machine Learning; Reinforcement Learning; X-FEL imaging; RANDOM FUNCTION ITERATIONS; tomography

摘要

We apply a recently developed framework for analyzing the convergence of stochastic algorithms to the general problem of large-scale nonconvex composite optimization more generally, and nonconvex likelihood maximization in particular. Our theory is demonstrated on a stochastic gradient descent algorithm for determining the electron density of a molecule from random samples of its scattering amplitude. Numerical results on an idealized synthetic example provide a proof of concept. The algorithm we use is just one of a wide range of possibilities, all of which can be formulated abstractly as random function iterations. Our framework provides a basis for evaluating and comparing different numerical strategies. While this case study is very specific, it shares a structure that transfers easily to many problems of current interest, particularly in machine learning.