Data-driven inverse optimization with imperfect information

Data-driven inverse optimization with imperfect information

Mohajerin Esfahani, P. (TU Delft Team Tamas Keviczky)
Shafieezadeh-Abadeh, Soroosh (Swiss Federal Institute of Technology)
Hanasusanto, Grani A. (The University of Texas at Austin)
Kuhn, Daniel (Swiss Federal Institute of Technology)

2018

In data-driven inverse optimization an observer aims to learn the preferences of an agent who solves a parametric optimization problem depending on an exogenous signal. Thus, the observer seeks the agent’s objective function that best explains a historical sequence of signals and corresponding optimal actions. We focus here on situations where the observer has imperfect information, that is, where the agent’s true objective function is not contained in the search space of candidate objectives, where the agent suffers from bounded rationality or implementation errors, or where the observed signal-response pairs are corrupted by measurement noise. We formalize this inverse optimization problem as a distributionally robust program minimizing the worst-case risk that the predicted decision (i.e., the decision implied by a particular candidate objective) differs from the agent’s actual response to a random signal. We show that our framework offers rigorous out-of-sample guarantees for different loss functions used to measure prediction errors and that the emerging inverse optimization problems can be exactly reformulated as (or safely approximated by) tractable convex programs when a new suboptimality loss function is used. We show through extensive numerical tests that the proposed distributionally robust approach to inverse optimization attains often better out-of-sample performance than the state-of-the-art approaches.

http://resolver.tudelft.nl/uuid:aef8f048-d693-4a81-8651-04d5afcce299

https://doi.org/10.1007/s10107-017-1216-6

2018-06-07

0025-5610

Mathematical Programming, 167 (1), 191-234

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Institutional Repository

journal article

© 2018 P. Mohajerin Esfahani, Soroosh Shafieezadeh-Abadeh, Grani A. Hanasusanto, Daniel Kuhn