Interior Point Solving for LP-based prediction+optimisation

Research output: Chapter in Book/Report/Conference proceedingConference paper

Abstract

Solving optimization problems is the key to decision making in many real-life analytics applications. However, the coefficients of the optimization problems are often uncertain and dependent on external factors, such as future demand or energy or stock prices. Machine learning (ML) models, especially neural networks, are increasingly being used to estimate these coefficients in a data-driven way. Hence, end-to-end predict-and-optimize approaches, which consider how effective the predicted values are to solve the optimization problem, have received increasing attention. In case of integer linear programming problems, a popular approach to overcome their non-differentiabilty is to add a quadratic penalty term to the continuous relaxation, such that results from differentiating over quadratic programs can be used. Instead we investigate the use of the more principled logarithmic barrier term, as widely used in interior point solvers for linear programming. Specifically, instead of differentiating the KKT conditions, we consider the homogeneous self-dual formulation of the LP and we show the relation between the interior point step direction and corresponding gradients needed for learning. Finally our empirical experiments demonstrate our approach performs as good as if not better than the state-of-the-art QPTL (Quadratic Programming task loss) formulation of Wilder et al. [29] and SPO approach of Elmachtoub and Grigas [12].

Original languageEnglish
Title of host publicationInterior Point Solving for LP-based prediction+optimisation
Number of pages15
Volume2020-December
Publication statusPublished - 9 Dec 2020
EventNeural Information Processing Systems, 2020: Online Conference - Online
Duration: 6 Dec 202012 Dec 2020
https://neurips.cc/virtual/2020/public/index.html

Publication series

NameAdvances in Neural Information Processing Systems
ISSN (Print)1049-5258

Conference

ConferenceNeural Information Processing Systems, 2020
Period6/12/2012/12/20
Internet address

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