Data-driven inverse optimization with imperfect information

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 optim...

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Bibliographic Details
Published in:Mathematical programming Vol. 167; no. 1; pp. 191 - 234
Main Authors: Mohajerin Esfahani, Peyman, Shafieezadeh-Abadeh, Soroosh, Hanasusanto, Grani A., Kuhn, Daniel
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2018
Springer Nature B.V
Subjects:
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Economic models
Full Length Paper
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Mathematics of Computing
Noise measurement
Numerical Analysis
Optimization
Predictions
Robustness (mathematics)
Theoretical
90C25 Convex programming
90C47 Minimax problems
C15 Stochastic programming
ISSN:0025-5610, 1436-4646
Online Access:Get full text
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Summary: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.
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-017-1216-6