# A Pareto Dominance Principle for Data-Driven Optimization

arXiv: https://arxiv.org/abs/2010.06606 · HTML: https://mlsanity.com/paper/2010.06606/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Oct 2020.

## Built on by (most cited first, 7 of 7)

- [Robust Generalization despite Distribution Shift via Minimum Discriminating Information](https://mlsanity.com/paper/2106.04443/) (2021)
- [Distributionally Robust Optimization with Markovian Data](https://mlsanity.com/paper/2106.06741/) (2021)
- [Towards Optimal Offline Reinforcement Learning](https://mlsanity.com/paper/2503.12283/) (2025)
- [Optimal Confidence Intervals via Moderate Deviations Theory](https://mlsanity.com/paper/2305.14496/) (2023)
- [MMORF: A Multi-agent Framework for Designing Multi-objective Retrosynthesis Planning Systems](https://mlsanity.com/paper/2604.05075/) (2026)
- [Optimize-via-Predict: Realizing out-of-sample optimality in data-driven optimization](https://mlsanity.com/paper/2309.11147/) (2023)
- [Achieving First-Order Statistical Improvements in Data-Driven Optimization: From No-Free-Lunch to Amplified Decision Perturbation](https://mlsanity.com/paper/2608.04312/) (2026)

## Abstract (arXiv)

We propose a statistically optimal approach to construct data-driven decisions for stochastic optimization problems. Fundamentally, a data-driven decision is simply a function that maps the available training data to a feasible action. It can always be expressed as the minimizer of a surrogate optimization model constructed from the data. The quality of a data-driven decision is measured by its out-of-sample risk. An additional quality measure is its out-of-sample disappointment, which we define as the probability that the out-of-sample risk exceeds the optimal value of the surrogate optimization model. An ideal data-driven decision should minimize the out-of-sample risk simultaneously with respect to every conceivable probability measure as the true measure is unkown. Unfortunately, such ideal data-driven decisions are generally unavailable. This prompts us to seek data-driven decisions that minimize the in-sample risk subject to an upper bound on the out-of-sample disappointment. We prove that such Pareto-dominant data-driven decisions exist under conditions that allow for interesting applications: the unknown data-generating probability measure must belong to a parametric ambiguity set, and the corresponding parameters must admit a sufficient statistic that satisfies a large deviation principle. We can further prove that the surrogate optimization model must be a distributionally robust optimization problem constructed from the sufficient statistic and the rate function of its large deviation principle. Hence the optimal method for mapping data to decisions is to solve a distributionally robust optimization model. Maybe surprisingly, this result holds even when the training data is non-i.i.d. Our analysis reveals how the structural properties of the data-generating stochastic process impact the shape of the ambiguity set underlying the optimal distributionally robust model.