Learning to Solve Constrained Bilevel Control Co-Design Problems

TL;DR

This paper introduces a framework that uses machine learning to efficiently approximate solutions to complex bilevel optimization problems, including control system co-design, which are traditionally difficult to solve quickly.

Contribution

It extends Learning to Optimize methods to bilevel programs by leveraging differentiation techniques, enabling fast approximation of solutions for challenging problems.

Findings

Successfully applied to synthetic bilevel problems

Effective in control system co-design scenarios

Neural networks provide accurate approximations

Abstract

Learning to Optimize (L2O) is a subfield of machine learning (ML) in which ML models are trained to solve parametric optimization problems. The general goal is to learn a fast approximator of solutions to constrained optimization problems, as a function of their defining parameters. Prior L2O methods focus almost entirely on single-level programs, in contrast to the bilevel programs, whose constraints are themselves expressed in terms of optimization subproblems. Bilevel programs have numerous important use cases but are notoriously difficult to solve, particularly under stringent time demands. This paper proposes a framework for learning to solve a broad class of challenging bilevel optimization problems, by leveraging modern techniques for differentiation through optimization problems. The framework is illustrated on an array of synthetic bilevel programs, as well as challenging control system co-design problems, showing how neural networks can be trained as efficient approximators of parametric bilevel optimization.