A distributional interpretation of robust optimization

Huan Xu, Constantine Caramanis, Shie Mannor

Research output: Contribution to journalArticlepeer-review


Motivated by data-driven decision making and sampling problems, we investigate probabilistic interpretations of robust optimization (RO). We establish a connection between RO and distributionally robust stochastic programming (DRSP), showing that the solution to any RO problem is also a solution to a DRSP problem. Specifically, we consider the case where multiple uncertain parameters belong to the same fixed dimensional space and find the set of distributions of the equivalent DRSP problem. The equivalence we derive enables us to construct RO formulations for sampled problems (as in stochastic programming and machine learning) that are statistically consistent, even when the original sampled problem is not. In the process, this provides a systematic approach for tuning the uncertainty set. The equivalence further provides a probabilistic explanation for the common shrinkage heuristic, where the uncertainty set used in an RO problem is a shrunken version of the original uncertainty set.

Original languageEnglish
Pages (from-to)95-110
Number of pages16
JournalMathematics of Operations Research
Issue number1
StatePublished - Feb 2012


  • Consistency
  • Distributionally robust stochastic programming
  • Kernel density estimator
  • Machine learning
  • Robust optimization

All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • General Mathematics
  • Management Science and Operations Research


Dive into the research topics of 'A distributional interpretation of robust optimization'. Together they form a unique fingerprint.

Cite this