Learning Parametric Convex Functions

About

A parametrized convex function depends on a variable and a parameter, and is convex in the variable for any valid value of the parameter. Such functions can be used to specify parametrized convex optimization problems, i.e., a convex optimization family, in domain specific languages for convex optimization. In this paper we address the problem of fitting a parametrized convex function that is compatible with disciplined programming, to some given data. This allows us to fit a function arising in a convex optimization formulation directly to observed or simulated data. We demonstrate our open-source implementation on several examples, ranging from illustrative to practical.

Maximilian Schaller, Alberto Bemporad, Stephen Boyd · 2025

Related benchmarks

Task	Dataset	Result
Downstream Optimization	box_logsumexp d=50 (test)	Test Relative Error0.029	7
Learning Convex Surrogate Functions	box_logsumexp d=10	Test Relative Error0.032	7
Learning Convex Surrogate Functions	box_socp d=10	Test RelErr6.2	7
Learning Convex Surrogate Functions	budget_huber d=10	Test Relative Error4.1	7
Learning Convex Surrogate Functions	simplex_logistic d=10	Test Relative Error0.4	7
Learning Convex Surrogate Functions	simplex_socp d=10	Test Relative Error6.5	7
Learning Convex Surrogate Functions	budget_twocone_socp d=10	Test Relative Error0.038	7
Downstream Optimization	box_socp d=50 (test)	Test Relative Error4.1	7
box_logsumexp optimization	Experiment d = 20 3	Test Relative Error0.031	4