Predict-then-Optimize v/s Probabilistic Approximations: Tackling Uncertainties and Error Propagation

Priya Shanmugasundaram, Saurabh Jha, Kumar Muthuraman

Keywords: Convex Optimization, Predict-then-Optimize, Optimization

TL;DR: A novel method to integrate predictions from machine learning systems into optimization problems.

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.

Submission Number: 30