Contextual Inverse Optimization: Offline and Online Learning

Omar Besbes (), Yuri Fonseca () and Ilan Lobel ()
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Omar Besbes: Decision, Risk and Operations, Graduate School of Business, Columbia University, New York, New York 10027
Yuri Fonseca: Decision, Risk and Operations, Graduate School of Business, Columbia University, New York, New York 10027
Ilan Lobel: Technology, Operations, and Statistics, Stern School of Business, New York University, New York, New York 10012

Operations Research, 2025, vol. 73, issue 1, 424-443

Abstract: We study the problems of offline and online contextual optimization with feedback information, where instead of observing the loss, we observe, after the fact, the optimal action an oracle with full knowledge of the objective function would have taken. We aim to minimize regret, which is defined as the difference between our losses and the ones incurred by an all-knowing oracle. In the offline setting, the decision maker has information available from past periods and needs to make one decision, whereas in the online setting, the decision maker optimizes decisions dynamically over time based a new set of feasible actions and contextual functions in each period. For the offline setting, we characterize the optimal minimax policy, establishing the performance that can be achieved as a function of the underlying geometry of the information induced by the data. In the online setting, we leverage this geometric characterization to optimize the cumulative regret. We develop an algorithm that yields the first regret bound for this problem that is logarithmic in the time horizon. Finally, we show via simulation that our proposed algorithms outperform previous methods from the literature.

Keywords: Optimization; contextual optimization; online optimization; imitation learning; inverse optimization; learning from revealed preferences; data-driven decision making (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:73:y:2025:i:1:p:424-443

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