papersurveydrorahimianmehrotraojmo2022

Rahimian, W. & Mehrotra (2022) — Distributionally Robust Optimization: A Review

Citation. Rahimian, H. & Mehrotra, S. (2022) "Distributionally Robust Optimization: A Review". Open Journal of Mathematical Optimization 3. DOI: 10.5802/ojmo.15. arXiv:1908.05659 (initial version 13 Aug 2019).

Source archive. raw/papers/201908-distributionally-robust-optimization-review/{paper.pdf, extracted.md}.

Summary. summaries/201908-distributionally-robust-optimization-review/201908-distributionally-robust-optimization-review.

Why this is a landmark

A 90+ page survey of distributionally robust optimisation (DRO) organised around:

  1. Four problem formulations — stochastic optimisation (SO), robust optimisation (RO), chance-constrained optimisation (CCO), risk-averse optimisation — shown to be special cases of a single DRO primal with different choices of functional R_P and ambiguity set \mathcal P.
  2. Two solution techniques — cutting-surface / exchange method, and dual reformulation. The latter dominates the recent literature.
  3. Four ambiguity-set families — discrepancy-based (Wasserstein, \phi-divergence, total variation, Prohorov, \zeta-structure, \ell_p, contamination), moment-based (Chebyshev, Delage–Ye, generalised moment, moment-matrix), shape-preserving, kernel-based.
  4. Data-driven calibration with finite-sample statistical guarantees — particularly the Mohajerin Esfahani–Kuhn Wasserstein-ball result, which gives a closed-form confidence radius \epsilon_N(\beta).
  5. Toolboxes — ROME, ROC, AROMA, XProg — implementing the resulting SDP / SOCP / LP reformulations.

Conceptual impact on the wiki

The survey is the primary source for four concept pages in the wiki:

These pages adopt the survey's taxonomy and notation, and use its \epsilon_N(\beta) formula as the canonical example of a deployable data-driven DRO calibration.

Open questions surfaced by the review

  • How big should \epsilon be? The Mohajerin Esfahani–Kuhn finite-sample formula is the only principled answer in the literature; in practice, cross-validation is still common. The trade-off between statistical confidence and out-of-sample performance is poorly understood in production risk models.
  • DRO vs M-estimators. For linear-regression-style losses, the survey shows that Wasserstein-DRO recovers Huber / LASSO / quantile regression as special cases. The mapping between DRO radius \epsilon and the regularisation strength \lambda is explicit but rarely exploited in practice; quant teams typically pick \lambda by cross-validation.
  • Wasserstein with learned cost. Blanchet et al.'s data-driven transportation cost c is a recent advance (2019); its impact on portfolio / stat-arb performance is unmeasured.
  • Multistage time consistency. The survey flags the open problem of time-consistent multistage DRO with Wasserstein nested distance; only partial results exist (Xin & Goldberg 2018 for the newsvendor).

See also