In this paper, we survey the primary research on the theory and applications of
distributionally robust optimization (DRO). We start with reviewing the modeling power and
computational attractiveness of DRO approaches, induced by the ambiguity sets structure
and tractable robust counterpart reformulations. Next, we summarize the efficient solution
methods, out-of-sample performance guarantee, and convergence analysis. Then, we
illustrate some applications of DRO in machine learning and operations research, and …

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 …