Scaled Neural Multiplicative Model for Tractable Optimization

Drishya Giri, Kenneth Kuhn, Aravind Chiruvelli

Keywords: Input Convex Neural Networks, Shape Constrained Models, Shelf Space Optimization

Abstract: Challenging decision problems in retail and beyond are often solved using the predict-then-optimize paradigm. An initial effort to develop and parameterize a model of an uncertain environment is followed by a separate effort to identify the best possible solution of an optimization problem. Linear models are often used to ensure optimization problems are tractable. Remarkably accurate Deep Neural Network (DNN) models have recently been developed for various prediction tasks. Such models have been shown to scale to large datasets without loss of accuracy and with good computational performance. It can, however, be challenging to formulate tractable optimization problems based on DNN models. In this work we consider the problem of shelf space allocation for retail stores using DNN models. We highlight the trade-off between predictive performance and the tractability of optimization problems. We introduce a Scaled Neural Multiplicative Model (SNMM) with shape constraints for demand learning that leads to a tractable optimization formulation. Although, this work focuses on a specific application, the formulation of the models are general enough such that they can be extended to many real world applications.

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