Regret Bounds and Experimental Design for Estimate-then-Optimize

• URL: http://arxiv.org/abs/2210.15576v1
• Date: Thu, 27 Oct 2022 16:13:48 GMT
• Title: Regret Bounds and Experimental Design for Estimate-then-Optimize
• Authors: Samuel Tan, Peter I. Frazier
• Abstract summary: In practical applications, data is used to make decisions in two steps: estimation and optimization. Errors in the estimation step can lead estimate-then-optimize to sub-optimal decisions. We provide a novel bound on this regret for smooth and unconstrained optimization problems.
• Score: 9.340611077939828
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In practical applications, data is used to make decisions in two steps: estimation and optimization. First, a machine learning model estimates parameters for a structural model relating decisions to outcomes. Second, a decision is chosen to optimize the structural model's predicted outcome as if its parameters were correctly estimated. Due to its flexibility and simple implementation, this ``estimate-then-optimize'' approach is often used for data-driven decision-making. Errors in the estimation step can lead estimate-then-optimize to sub-optimal decisions that result in regret, i.e., a difference in value between the decision made and the best decision available with knowledge of the structural model's parameters. We provide a novel bound on this regret for smooth and unconstrained optimization problems. Using this bound, in settings where estimated parameters are linear transformations of sub-Gaussian random vectors, we provide a general procedure for experimental design to minimize the regret resulting from estimate-then-optimize. We demonstrate our approach on simple examples and a pandemic control application.

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