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An Online-Learning Approach to Inverse Optimization

Andreas Bärmann(Andreas.Baermann***at***math.uni-erlangen.de)
Alexander Martin(Alexander.Martin***at***math.uni-erlangen.de)
Sebastian Pokutta(Sebastian.Pokutta***at***isye.gatech.edu)
Oskar Schneider(Oskar.Schneider***at***fau.de)

Abstract: In this paper, we demonstrate how to learn the objective function of a decision-maker while only observing the problem input data and the decision-maker’s corresponding decisions over multiple rounds. Our approach is based on online learning and works for linear objectives over arbitrary feasible sets for which we have a linear optimization oracle. As such, it generalizes previous approaches based on KKT-system decomposition and dualization. The two exact algorithms we present – based on multiplicative weights updates and online gradient descent respectively – converge at a rate of O(1/sqrt(T)) and thus allow taking decisions which are essentially as good as those of the observed decision-maker already after relatively few observations. We also discuss several useful generalizations, such as the approximate learning of non-linear objective functions and the case of suboptimal observations. Finally, we show the effectiveness and possible applications of our methods in a broad computational study

Keywords: Learning Objective Functions, Online Learning, Multiplicative Weights Update Algorithm, Online Gradient Descent, Mixed-Integer-Programming

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Other Topics (Game Theory )

Category 3: Integer Programming

Citation:

Download: [PDF]

Entry Submitted: 10/30/2018
Entry Accepted: 10/30/2018
Entry Last Modified: 10/30/2018

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