# Convex Optimal Uncertainty Quantification

arXiv: https://arxiv.org/abs/1311.7130 · HTML: https://mlsanity.com/paper/1311.7130/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Nov 2013.

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

- [Differential Privacy via Distributionally Robust Optimization](https://mlsanity.com/paper/2304.12681/) (2023)

## Abstract (arXiv)

Optimal uncertainty quantification (OUQ) is a framework for numerical extreme-case analysis of stochastic systems with imperfect knowledge of the underlying probability distribution. This paper presents sufficient conditions under which an OUQ problem can be reformulated as a finite-dimensional convex optimization problem, for which efficient numerical solutions can be obtained. The sufficient conditions include that the objective function is piecewise concave and the constraints are piecewise convex. In particular, we show that piecewise concave objective functions may appear in applications where the objective is defined by the optimal value of a parameterized linear program.