Distributionally Robust Optimization: A Review

TL;DR

This paper reviews the development and key concepts of distributionally robust optimization (DRO), highlighting its connections with robust optimization, risk management, and regularization in statistical learning.

Contribution

It provides a comprehensive survey of DRO, clarifying its theoretical foundations, practical applications, and relationships with related optimization frameworks.

Findings

DRO unifies robust and risk-averse optimization approaches.

Recent advances have expanded DRO's applications in machine learning.

The survey clarifies the theoretical and practical significance of DRO.

Abstract

The concepts of risk-aversion, chance-constrained optimization, and robust optimization have developed significantly over the last decade. Statistical learning community has also witnessed a rapid theoretical and applied growth by relying on these concepts. A modeling framework, called distributionally robust optimization (DRO), has recently received significant attention in both the operations research and statistical learning communities. This paper surveys main concepts and contributions to DRO, and its relationships with robust optimization, risk-aversion, chance-constrained optimization, and function regularization.