# Efficient Data-Driven Optimization with Noisy Data

arXiv: https://arxiv.org/abs/2102.04363 · HTML: https://mlsanity.com/paper/2102.04363/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 55 references that are in the map.
- First posted on arXiv 8 Feb 2021.

## Builds on (most cited first, 11 of 11)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations](https://mlsanity.com/paper/1505.05116/) (2015)
- [Statistics of Robust Optimization: A Generalized Empirical Likelihood Approach](https://mlsanity.com/paper/1610.03425/) (2016)
- [Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning](https://mlsanity.com/paper/1908.08729/) (2019)
- [Data-Driven Robust Optimization](https://mlsanity.com/paper/1401.0212/) (2013)
- [Regularization via Mass Transportation](https://mlsanity.com/paper/1710.10016/) (2017)
- [Sinkhorn Divergences for Unbalanced Optimal Transport](https://mlsanity.com/paper/1910.12958/) (2019)
- [From Data to Decisions: Distributionally Robust Optimization is Optimal](https://mlsanity.com/paper/1704.04118/) (2017)
- [Recovering Best Statistical Guarantees via the Empirical Divergence-based Distributionally Robust Optimization](https://mlsanity.com/paper/1605.09349/) (2016)
- [Tractable Reformulations of Distributionally Robust Two-stage Stochastic Programs with ∞-Wasserstein Distance](https://mlsanity.com/paper/1908.08454/) (2019)

## Built on by (most cited first, 1 of 1)

- [From Distributional Robustness to Robust Statistics: A Confidence Sets Perspective](https://mlsanity.com/paper/2410.14008/) (2024)

## Abstract (arXiv)

Classical Kullback-Leibler or entropic distances are known to enjoy certain desirable statistical properties in the context of decision-making with noiseless data. However, in most practical situations the data available to a decision maker is subject to a certain amount of measurement noise. We hence study here data-driven prescription problems in which the data is corrupted by a known noise source. We derive efficient data-driven formulations in this noisy regime and indicate that they enjoy an entropic optimal transport interpretation. Finally, we show that these efficient robust formulations are tractable in several interesting settings by exploiting a classical representation result by Strassen.