Objective-Aligned Regression for Two-Stage Linear Programs

28 Pages Posted: 23 Oct 2019

See all articles by Alexander Estes

Alexander Estes

University of Minnesota - Institute for Mathematics and its Applications

Jean-Philippe Richard

Industrial and Systems Engineering, University of Minnesota

Date Written: October 14, 2019

Abstract

We study an approach to regression that we call objective-aligned fitting, which is applicable when the regression model is used to predict uncertain parameters of some objective problem. Rather than minimizing a typical loss function, such as squared error, we approximately minimize the objective value of the resulting solutions to the nominal optimization problem. While previous work on objective-aligned fitting has tended to focus on uncertainty in the objective function, we consider the case in which the nominal optimization problem is a two-stage linear program with uncertainty in the right-hand side. We define the objective-aligned loss function for the problem and prove structural properties concerning this loss function. Since the objective-aligned loss function is generally non-convex, we develop a convex approximation. We propose a method for fitting a linear regression model to the convex approximation of the objective-aligned loss. Computational results indicate that this procedure can lead to higher-quality solutions than existing regression procedures.

Keywords: stochastic optimization, optimization under uncertainty, linear programming, regression, objective-aligned fitting

JEL Classification: C44

Suggested Citation

Estes, Alexander and Richard, Jean-Philippe, Objective-Aligned Regression for Two-Stage Linear Programs (October 14, 2019). Available at SSRN: https://ssrn.com/abstract=3469897 or http://dx.doi.org/10.2139/ssrn.3469897

Alexander Estes (Contact Author)

University of Minnesota - Institute for Mathematics and its Applications ( email )

425 Lind Hall
207 Church St SE
Minneapolis, MN 55455
United States

HOME PAGE: http://asestes1.github.io

Jean-Philippe Richard

Industrial and Systems Engineering, University of Minnesota ( email )

111 Church St SE
Minneapolis, MN 55455
United States

HOME PAGE: http://www.isye.umn.edu/faculty/richard.shtml

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
33
Abstract Views
182
PlumX Metrics