73 research outputs found
Data-driven chance constrained programs over wasserstein balls
We provide an exact deterministic reformulation for data-driven, chance-constrained programs over Wasserstein balls. For individual chance constraints as well as joint chance constraints with right-hand-side uncertainty, our reformulation amounts to a mixed-integer conic program. In the special case of a Wasserstein ball with the 1-norm or the ∞-norm, the cone is the nonnegative orthant, and the chance-constrained program can be reformulated as a mixed-integer linear program. Our reformulation compares favorably to several state-of-the-art data-driven optimization schemes in our numerical experiments
Data-Driven Chance Constrained Programs over Wasserstein Balls
We provide an exact deterministic reformulation for data-driven chance
constrained programs over Wasserstein balls. For individual chance constraints
as well as joint chance constraints with right-hand side uncertainty, our
reformulation amounts to a mixed-integer conic program. In the special case of
a Wasserstein ball with the -norm or the -norm, the cone is the
nonnegative orthant, and the chance constrained program can be reformulated as
a mixed-integer linear program. Our reformulation compares favourably to
several state-of-the-art data-driven optimization schemes in our numerical
experiments.Comment: 25 pages, 9 figure
Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations
We consider stochastic programs where the distribution of the uncertain
parameters is only observable through a finite training dataset. Using the
Wasserstein metric, we construct a ball in the space of (multivariate and
non-discrete) probability distributions centered at the uniform distribution on
the training samples, and we seek decisions that perform best in view of the
worst-case distribution within this Wasserstein ball. The state-of-the-art
methods for solving the resulting distributionally robust optimization problems
rely on global optimization techniques, which quickly become computationally
excruciating. In this paper we demonstrate that, under mild assumptions, the
distributionally robust optimization problems over Wasserstein balls can in
fact be reformulated as finite convex programs---in many interesting cases even
as tractable linear programs. Leveraging recent measure concentration results,
we also show that their solutions enjoy powerful finite-sample performance
guarantees. Our theoretical results are exemplified in mean-risk portfolio
optimization as well as uncertainty quantification.Comment: 42 pages, 10 figure
Conic Reformulations for Kullback-Leibler Divergence Constrained Distributionally Robust Optimization and Applications
In this paper, we consider a distributionally robust optimization (DRO) model
in which the ambiguity set is defined as the set of distributions whose
Kullback-Leibler (KL) divergence to an empirical distribution is bounded.
Utilizing the fact that KL divergence is an exponential cone representable
function, we obtain the robust counterpart of the KL divergence constrained DRO
problem as a dual exponential cone constrained program under mild assumptions
on the underlying optimization problem. The resulting conic reformulation of
the original optimization problem can be directly solved by a commercial conic
programming solver. We specialize our generic formulation to two classical
optimization problems, namely, the Newsvendor Problem and the Uncapacitated
Facility Location Problem. Our computational study in an out-of-sample analysis
shows that the solutions obtained via the DRO approach yield significantly
better performance in terms of the dispersion of the cost realizations while
the central tendency deteriorates only slightly compared to the solutions
obtained by stochastic programming
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