# Data-Pooling in Stochastic Optimization

arXiv: https://arxiv.org/abs/1906.00255 · HTML: https://mlsanity.com/paper/1906.00255/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jun 2019.

## Built on by (most cited first, 14 of 14)

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- [Contextual Optimization under Covariate Shift: A Robust Approach by Intersecting Wasserstein Balls](https://mlsanity.com/paper/2406.02426/) (2024)
- [Regret Equals Covariance: A Closed-Form Characterization for Stochastic Optimization](https://mlsanity.com/paper/2605.14019/) (2026)
- [Adaptive Data Fusion for Multi-task Non-smooth Optimization](https://mlsanity.com/paper/2210.12334/) (2022)
- [Survey of Data-driven Newsvendor: Unified Analysis and Spectrum of Achievable Regrets](https://mlsanity.com/paper/2409.03505/) (2024)
- [LLM-Inspired Pretrain-Then-Finetune for Small-Data, Large-Scale Optimization](https://mlsanity.com/paper/2602.03690/) (2026)
- [Robust Data-driven Prescriptiveness Optimization](https://mlsanity.com/paper/2306.05937/) (2023)
- [Optimal data pooling for shared learning in maintenance operations](https://mlsanity.com/paper/2308.12670/) (2023)
- [Stability Regularized Cross-Validation](https://mlsanity.com/paper/2505.06927/) (2025)
- [Learning Shortest Paths When Data is Scarce](https://mlsanity.com/paper/2601.03629/) (2026)

## Abstract (arXiv)

Managing large-scale systems often involves simultaneously solving thousands of unrelated stochastic optimization problems, each with limited data. Intuition suggests 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 non-convex, non-smooth 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.