Learning Parametric Convex Functions

TL;DR

This paper introduces a method for fitting parametrized convex functions to data, enabling direct modeling of convex optimization problems within domain-specific languages, with practical open-source implementations demonstrated.

Contribution

It presents a novel approach for learning parametrized convex functions compatible with disciplined programming, bridging data fitting and convex optimization modeling.

Findings

Successfully fit parametrized convex functions to various datasets

Demonstrated practical applications with open-source tools

Enabled direct modeling of convex optimization problems from data

Abstract

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.