REVIEW 7 cited by
Distributionally Robust Stochastic Optimization with Wasserstein Distance
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
read the original abstract
Distributionally robust stochastic optimization (DRSO) is an approach to optimization under uncertainty in which, instead of assuming that there is a known true underlying probability distribution, one hedges against a chosen set of distributions. In this paper we first point out that the set of distributions should be chosen to be appropriate for the application at hand, and that some of the choices that have been popular until recently are, for many applications, not good choices. We next consider sets of distributions that are within a chosen Wasserstein distance from a nominal distribution. Such a choice of sets has two advantages: (1) The resulting distributions hedged against are more reasonable than those resulting from other popular choices of sets. (2) The problem of determining the worst-case expectation over the resulting set of distributions has desirable tractability properties. We derive a strong duality reformulation of the corresponding DRSO problem and construct approximate worst-case distributions explicitly via the first-order optimality conditions of the dual problem. Our contributions are four-fold. (i) We identify necessary and sufficient conditions for the existence of a worst-case distribution, which are naturally related to the growth rate of the objective function. (ii) We show that the worst-case distributions resulting from an appropriate Wasserstein distance have a concise structure and a clear interpretation. (iii) Using this structure, we show that data-driven DRSO problems can be approximated to any accuracy by robust optimization problems, and thereby many DRSO problems become tractable by using tools from robust optimization. (iv) Our strong duality result holds in a very general setting. As examples, we show that it can be applied to infinite-dimensional process control and intensity estimation for point processes.
Forward citations
Cited by 7 Pith papers
-
Cross-Dock Door Design under Uncertainty: A two-stage DRO-based lower- and upper-bounding scheme
A scenario-cluster matheuristic solves a two-stage distributionally robust cross-dock door design model, giving bounds within 2.4 to 9.7 percent of a lower bound and matching or improving on CPLEX and Gurobi on the te...
-
Tractable Reformulations of Distributionally Robust Two-stage Stochastic Programs with $\infty-$Wasserstein Distance
Under sign conditions on the technology matrix, the worst-case expected recourse cost in two-stage distributionally robust programs with infinity-Wasserstein ambiguity is exactly a finite linear or conic program with ...
-
Uncovering expert objectives in production planning via inverse optimization: An industrial case study
Inverse optimization of a mixed-integer production planning model on 50 training plans reveals that Dow planners weight avoiding understock and stable cycle lengths most heavily.
-
Gradient Flow Sampler-based Distributionally Robust Optimization
Entropy-regularized Wasserstein DRO can be solved by sampling from a Gibbs worst-case distribution with gradient-flow samplers, giving new WFR/SVGD algorithms and a principled recovery of WRM.
-
Data-Driven Distributionally Robust Optimization for Long-Term Contract vs. Spot Allocation Decisions: Application to Electricity Markets
For a price-taking electricity generator, CVaR and Wasserstein distributionally robust models produce similar aggregate contract/spot tradeoff curves when risk parameters are matched, but they differ in per-node allocation.
-
Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning
Wasserstein distributionally robust optimization yields data-driven decisions that are computable as convex programs and have finite-sample out-of-sample guarantees, and this tutorial unifies the theory with machine l...
-
Distributionally Robust Optimization: A Review
A broad review of distributionally robust optimization that organizes the literature by ambiguity-set type and connects DRO to robust optimization, risk aversion, chance constraints, and regularization.
Discussion (0). Continue with ORCID to comment.