Work

Empirical Risk Minimization for Risk-Neutral Composite Optimal Control with Applications to Bang-Bang Control

Year: 2026

Type: article

Abstract: . Nonsmooth composite optimization problems under uncertainty are prevalent in various scientific and engineering applications. We consider risk-neutral composite optimal control problems, where the objective function is the sum of a potentially nonconvex expectation function and a nonsmooth, convex function. To approximate the risk-neutral optimization problems, we use a Monte Carlo sample-based approach, study its asymptotic consistency, and derive nonasymptotic sample size estimates. Our analyses leverage problem structure commonly encountered in partial differential equation (PDE)–constrained optimization problems, including compact embeddings and growth conditions. We apply our findings to bang-bang-type optimal control problems and propose the use of a conditional gradient method to solve them effectively. We present numerical illustrations.

Source: SIAM/ASA Journal on Uncertainty Quantification

DOI: 10.1137/24m1690382

Authors: Johannes Milz, Daniel Walter

Institutions: Georgia Institute of Technology, Johannes Kepler University of Linz

Language: English

Topic: Risk and Portfolio Optimization

Subfield: Management Science and Operations Research

Field: Decision Sciences

Domain: Social Sciences

Open Access status: green

Funder: National Science Foundation

Award: Reliable data-driven optimization with complex physics-based systems