Contextual Inverse Optimization: Offline and Online Learning

60 Pages Posted: 10 Jun 2021 Last revised: 7 Mar 2022

See all articles by Omar Besbes

Omar Besbes

Columbia University - Columbia Business School, Decision Risk and Operations

Yuri Fonseca

Columbia University - Columbia Business School, Decision Risk and Operations

Ilan Lobel

New York University (NYU)

Date Written: June 9, 2021

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, while 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.

Keywords: contextual optimization, online optimization, imitation learning, inverse optimization, learning from revealed preferences, data-driven decision-making

Suggested Citation

Besbes, Omar and Fonseca, Yuri and Lobel, Ilan, Contextual Inverse Optimization: Offline and Online Learning (June 9, 2021). Columbia Business School Research Paper, Available at SSRN: https://ssrn.com/abstract=3863366 or http://dx.doi.org/10.2139/ssrn.3863366

Omar Besbes (Contact Author)

Columbia University - Columbia Business School, Decision Risk and Operations ( email )

New York, NY
United States

Yuri Fonseca

Columbia University - Columbia Business School, Decision Risk and Operations ( email )

New York, NY
United States

Ilan Lobel

New York University (NYU) ( email )

Bobst Library, E-resource Acquisitions
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New York, NY 10003-711
United States

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