Optimization with Trained Machine Learning Models Embedded

arXiv (Cornell University)

Abstract

Trained ML models are commonly embedded in optimization problems. In many cases, this leads to large-scale NLPs that are difficult to solve to global optimality. While ML models frequently lead to large problems, they also exhibit homogeneous structures and repeating patterns (e.g., layers in ANNs). Thus, specialized solution strategies can be used for large problem classes. Recently, there have been some promising works proposing specialized reformulations using mixed-integer programming or reduced space formulations. However, further work is needed to develop more efficient solution approaches and keep up with the rapid development of new ML model architectures.

Authors 3

1. Artur M. Schweidtmann

   Delft University of Technology

   Affiliation as printed

   Delft University of Technology , Department of Chemical Engineering , Van der Maasweg 9 , Delft 2629 HZ , The Netherlands

2. Dominik Bongartz Aachen Process Systems Engineering (AVT.SVT)

   RWTH Aachen University · KU Leuven

   Affiliation as printed

   Department of Chemical Engineering , KU Leuven , Celestijnenlaan 200F , 3001 Leuven , Belgium

   Process Systems Engineering (AVT.SVT) , RWTH Aachen University , Forckenbeckstr. 51 , 52074 Aachen , Germany

3. Alexander Mitsos Aachen Process Systems Engineering (AVT.SVT)

   RWTH Aachen University

   Affiliation as printed

   Process Systems Engineering (AVT.SVT) , RWTH Aachen University , Forckenbeckstr. 51 , 52074 Aachen , Germany