Predict-Then-Optimize V/s Probabilistic Approximations: Tackling Uncertainties and Error Propagation

Abstract

Proactive planning is a key necessity for busi- nesses to function efficiently under uncertain and unforeseen circumstances. Planning for the future involves solving optimization problems, which are often naturally convex or are modeled as con- vex approximations to facilitate computation. The primary source of uncertainties in the real world that business are dealing with (eg. demand) can- not be reasonably approximated by deterministic values. Hence deterministic convex optimization approximation do not not yield reasonable solu- tions. Classically, one relies on assumptions on the data generating process (like for eg. that de- mand is log normal) to formulate as a stochastic optimization problem. However, in today’s world, such major uncertainties are often best predicted by machine learning methods. In this paper, we propose a novel method to integrate predictions from machine learning systems and optimization steps for a specific context of a resource utilisa- tion problem that faces non-stationary incoming workload. The proposed solution is robust and shows improved performance against using the traditional point-predictions directly in the opti- mization. The proposed solution can be easily extended to different kind of machine learning methods and objective functions.