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Contextual Decision-making under Parametric Uncertainty and Data-driven Optimistic Optimization

Junyu Cao (junyu.cao***at***mccombs.utexas.edu)
Rui Gao (rui.gao***at***mccombs.utexas.edu)

Abstract: We consider decision-making problems with contextual information, in which the reward function involves uncertain parameters that can be predicted using covariates. To quantify the uncertainty of the reward, we propose a new parameter uncertainty set based on a supervised learning oracle. We show that the worst/best-case reward over the proposed parameter uncertainty set serves as a confidence bound on the reward by sizing the uncertainty set properly. Based on these results, we develop performance guarantees for robust contextual optimization in the offline setting, and propose data-driven optimistic optimization as a systematic tool for online contextual decision-making with provable performance guarantees.

Keywords: contextual optimization; joint learning and optimization; data-driven optimization; robust optimization; optimism principle

Category 1: Robust Optimization

Category 2: Stochastic Programming

Category 3: Applications -- Science and Engineering (Statistics )

Citation:

Download: [PDF]

Entry Submitted: 10/14/2021
Entry Accepted: 10/15/2021
Entry Last Modified: 10/15/2021

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