Data-driven inverse optimization with imperfect information

Peyman Mohajerin Esfahani, Soroosh Shafieezadeh-Abadeh, Grani A. Hanasusanto, Daniel Kuhn

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)191-234
Number of pages44
JournalMathematical Programming
Issue number1
StatePublished - Jan 1 2018
Externally publishedYes


  • 90C25 Convex programming
  • 90C47 Minimax problems
  • C15 Stochastic programming

ASJC Scopus subject areas

  • Software
  • Mathematics(all)


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