Statistical Optimization in High Dimensions - A Research Paper

Huan Xu, Constantine Caramanis, and Shie Mannor

Received: January 2014
Accepted: March 2016
Published Online: July 5, 2016

The paper deals with optimization problems whose parameters are known only approximately, based on noisy samples. In large-scale applications, the number of samples one can collect is typically of the same order of (or even less than) the dimensionality of the problem.

Three algorithms are proposed to address this setting, combining ideas from statistics, machine learning, and robust optimization.

The key ingredients of to the algorithms are dimensionality reduction techniques from machine learning, robust optimization, and concentration of measure tools from statistics.

http://pubsonline.informs.org/doi/abs/10.1287/opre.2016.1504