Mixed-Integer Convex Nonlinear Optimization with Gradient-Boosted Trees Embedded

Miten Mistry (), Dimitrios Letsios (), Gerhard Krennrich, Robert M. Lee and Ruth Misener ()
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Miten Mistry: Department of Computing, Imperial College London, South Kensington SW7 2AZ, United Kingdom
Dimitrios Letsios: Department of Computing, Imperial College London, South Kensington SW7 2AZ, United Kingdom
Gerhard Krennrich: BASF SE, Ludwigshafen am Rhein, Germany
Robert M. Lee: BASF SE, Ludwigshafen am Rhein, Germany
Ruth Misener: Department of Computing, Imperial College London, South Kensington SW7 2AZ, United Kingdom

INFORMS Journal on Computing, 2021, vol. 33, issue 3, 1103-1119

Abstract: Decision trees usefully represent sparse, high-dimensional, and noisy data. Having learned a function from these data, we may want to thereafter integrate the function into a larger decision-making problem, for example, for picking the best chemical process catalyst. We study a large-scale, industrially relevant mixed-integer nonlinear nonconvex optimization problem involving both gradient-boosted trees and penalty functions mitigating risk. This mixed-integer optimization problem with convex penalty terms broadly applies to optimizing pretrained regression tree models. Decision makers may wish to optimize discrete models to repurpose legacy predictive models or they may wish to optimize a discrete model that accurately represents a data set. We develop several heuristic methods to find feasible solutions and an exact branch-and-bound algorithm leveraging structural properties of the gradient-boosted trees and penalty functions. We computationally test our methods on a concrete mixture design instance and a chemical catalysis industrial instance.

Keywords: gradient-boosted trees; branch-and-bound; mixed-integer convex programming; decomposition; catalysis (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:orijoc:v:33:y:2021:i:3:p:1103-1119

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