Decision-Driven Regularization: A Blended Model for Predict-then-Optimize

46 Pages Posted: 17 Jun 2020 Last revised: 19 Jan 2023

See all articles by Gar Goei Loke

Gar Goei Loke

Durham University Business School

Qinshen Tang

Nanyang Business School, Nanyang Technological University

Yangge Xiao

National University of Singapore, Institue of Operations Research and Analytics

Date Written: February 1, 2022

Abstract

In contextual optimization, the decision-maker seeks optimal decisions to minimize a cost function, that varies based on observed features. This context is common in many business applications ranging from on-demand delivery and retail operations to portfolio optimization and inventory management. In this paper, we study the predict-then-optimize approach, which first learns how outcomes result from the features, and then selects optimal decisions based on these outcomes. We propose a principled manner to construct a regularization for forming the predictions, via the subsequent optimization problem of selecting decisions to minimize cost. We term our framework decision-driven regularization, which is a blended predict-then-optimize framework that carries both elements of predictive accuracy and decision quality, and is tractable. It also addresses ambiguity in the definition of the cost function, via a surrogate that depends on a new hyper-parameter. We additionally show that alternative perspectives for formulating the problem, namely robust optimization and regret minimization, lead to models that are equivalent to or can be naturally approximated to our proposed model. As a consequence, our framework generalizes models such as SPO+ in Elmachtoub and Grigas (2021). We present reasons for why improving predictive accuracy is insufficient in the contextual stochastic optimization setting, and can even be detrimental, to improving the quality of decisions. Our model is shown to be numerically superior to other benchmarks, such as OLS, SPO+, Lasso, and Ridge, in our synthetic studies.

Keywords: joint prediction and optimization, robust optimization, worst-case regret minimization, regularization, decision-making under uncertainty

JEL Classification: C44, C10

Suggested Citation

Loke, Gar Goei and Tang, Qinshen and Xiao, Yangge, Decision-Driven Regularization: A Blended Model for Predict-then-Optimize (February 1, 2022). Available at SSRN: https://ssrn.com/abstract=3623006 or http://dx.doi.org/10.2139/ssrn.3623006

Gar Goei Loke

Durham University Business School ( email )

Mill Hill Lane
Durham, DH1 3LB
United Kingdom

Qinshen Tang

Nanyang Business School, Nanyang Technological University ( email )

Singapore, 639798
Singapore

Yangge Xiao (Contact Author)

National University of Singapore, Institue of Operations Research and Analytics ( email )

Institute of Operations Research and Analytics
Innovation 4.0, #04-01, 3 Research Link
117602
Singapore

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