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Contextual Inverse Optimization: Offline and Online Learning
- Source :
- SSRN Electronic Journal.
- Publication Year :
- 2021
- Publisher :
- Elsevier BV, 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. Finally, we show via simulation that our proposed algorithms outperform previous methods from the literature.
- Subjects :
- FOS: Computer and information sciences
Computer Science - Machine Learning
History
Mathematical optimization
Polymers and Plastics
Logarithm
Computer science
media_common.quotation_subject
Machine Learning (stat.ML)
Regret
Time horizon
Minimax
Industrial and Manufacturing Engineering
Oracle
Machine Learning (cs.LG)
Optimization and Control (math.OC)
Statistics - Machine Learning
FOS: Mathematics
Leverage (statistics)
Business and International Management
Function (engineering)
Set (psychology)
Mathematics - Optimization and Control
media_common
Subjects
Details
- ISSN :
- 15565068
- Database :
- OpenAIRE
- Journal :
- SSRN Electronic Journal
- Accession number :
- edsair.doi.dedup.....28e44e39045446e2bf0781836a9458da