Work

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

Year: 2026

Type: article

Abstract: 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.

Source: Mathematical Programming

DOI: 10.1007/s10107-025-02319-9

Authors: D. Russell Luke, Steffen Schultze, Helmut Grubmüller

Institutions: University of Göttingen, Max Planck Institute for Multidisciplinary Sciences

Language: English

Topic: Stochastic Gradient Optimization Techniques

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funder: Deutsche Forschungsgemeinschaft