Data Pooling in Stochastic Optimization

Vishal Gupta () and Nathan Kallus ()
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Vishal Gupta: Data Science and Operations, USC Marshall School of Business, Los Angles, California 90089
Nathan Kallus: School of Operations Research and Information Engineering and Cornell Tech, Cornell University, New York, New York 10044

Management Science, 2022, vol. 68, issue 3, 1595-1615

Abstract: Managing large-scale systems often involves simultaneously solving thousands of unrelated stochastic optimization problems, each with limited data. Intuition suggests that one can decouple these unrelated problems and solve them separately without loss of generality. We propose a novel data-pooling algorithm called Shrunken-SAA that disproves this intuition. In particular, we prove that combining data across problems can outperform decoupling, even when there is no a priori structure linking the problems and data are drawn independently. Our approach does not require strong distributional assumptions and applies to constrained, possibly nonconvex, nonsmooth optimization problems such as vehicle-routing, economic lot-sizing, or facility location. We compare and contrast our results to a similar phenomenon in statistics (Stein’s phenomenon), highlighting unique features that arise in the optimization setting that are not present in estimation. We further prove that, as the number of problems grows large, Shrunken-SAA learns if pooling can improve upon decoupling and the optimal amount to pool, even if the average amount of data per problem is fixed and bounded. Importantly, we highlight a simple intuition based on stability that highlights when and why data pooling offers a benefit, elucidating this perhaps surprising phenomenon. This intuition further suggests that data pooling offers the most benefits when there are many problems, each of which has a small amount of relevant data. Finally, we demonstrate the practical benefits of data pooling using real data from a chain of retail drug stores in the context of inventory management.

Keywords: data-driven optimization; small-data; large-scale regime; shrinkage; James-Stein estimation (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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