Inverse Learning: A Data-driven Framework to Infer Optimizations Models

Farzin Ahmadi, Fardin Ganjkhanloo, Kimia Ghobadi

Published 2020-11-05Version 1

We consider the problem of inferring optimal solutions and unknown parameters of a partially-known constrained problem using a set of past decisions. We assume that the constraints of the original optimization problem are known while optimal decisions and the objective are to be inferred. In such situations, the quality of the optimal solution is evaluated in relation to the existing observations and the known parameters of the constrained problem. A method previously used in such settings is inverse optimization. This method can be used to infer the utility functions of a decision-maker and to find optimal solutions based on these inferred parameters indirectly. However, little effort has been made to generalize the inverse optimization methodology to data-driven settings to address the quality of the inferred optimal solutions. In this work, we present a data-driven inverse linear optimization framework (Inverse Learning) that aims to infer the optimal solution to an optimization problem directly based on the observed data and the existing known parameters of the problem. We validate our model on a dataset in the diet recommendation problem setting to find personalized diets for prediabetic patients with hypertension. Our results show that our model obtains optimal personalized daily food intakes that preserve the original data trends while providing a range of options to patients and providers. The results show that our proposed model is able to both capture optimal solutions with minimal perturbation from the given observations and, at the same time, achieve the inherent objectives of the original problem. We show an inherent trade-off in the quality of the inferred solutions with different metrics and provide insights into how a range of optimal solutions can be inferred in constrained environments.