Frameworks and results in distributionally robust optimization. (English) Zbl 1492.90109
Summary: The concepts of risk aversion, chance-constrained optimization, and robust optimization have developed significantly over the last decade. The 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 relationships with robust optimization, risk aversion, chance-constrained optimization, and function regularization. Various approaches to model the distributional ambiguity and their calibrations are discussed. The paper also describes the main solution techniques used to the solve the resulting optimization problems.
MSC:
| 90C15 | Stochastic programming |
| 90C17 | Robustness in mathematical programming |
| 90C22 | Semidefinite programming |
| 90C25 | Convex programming |
| 90C30 | Nonlinear programming |
| 90C34 | Semi-infinite programming |
| 90C90 | Applications of mathematical programming |
| 68T37 | Reasoning under uncertainty in the context of artificial intelligence |
| 68T05 | Learning and adaptive systems in artificial intelligence |
Keywords:
distributionally robust optimization; robust optimization; stochastic optimization; risk-averse optimization; chance-constrained optimization; statistical learningReferences:
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