Data-driven chance constrained stochastic program

Jiang, Ruiwei; Guan, Yongpei

doi:10.1007/s10107-015-0929-7

Cited by 416 publications

(320 citation statements)

References 46 publications

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“…We also set α = 20% and ρ = 10 in all numerical experiments, and we use the 1-norm to measure distances in the uncertainty space. Thus, · * is the ∞-norm, whereby (27) reduces to a linear program.…”

Section: Simulation Results: Portfolio Optimizationmentioning

confidence: 99%

“…For large Wasserstein radii ε, the term λε dominates the objective function of problem (27). Using standard epi-convergence results [42,Section 7.E], one can thus show that…”

Section: Mean-risk Portfolio Optimizationmentioning

confidence: 96%

“…Moment ambiguity sets contain all distributions that satisfy certain moment constraints, see for example [18,22,51] or the references therein. An attractive alternative is to define the ambiguity set as a ball in the space of probability distributions by using a probability distance function such as the Prohorov metric [20], the Kullback-Leibler divergence [25,27], or the Wasserstein metric [38,52] etc. Such metric-based ambiguity sets contain all distributions that are close to a nominal or most likely distribution with respect to the prescribed probability metric.…”

Section: Introductionmentioning

confidence: 99%

“…Subsequent work has focused on Kullback-Leibler ambiguity sets for discrete distributions with a fixed support, which offer additional modeling flexibility without sacrificing computational tractability [2,14]. It is also known that distributionally robust chance constraints involving a generic Kullback-Leibler ambiguity set are equivalent to the respective classical chance constraints under the nominal distribution but with a rescaled violation probability [26,27]. Moreover, closed-form counterparts of distributionally robust expectation constraints with Kullback-Leibler ambiguity sets have been derived in [25].…”

Section: Introductionmentioning

confidence: 99%

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Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable reformulations

2017

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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.Mathematics Subject Classification 90C15 Stochastic programming · 90C25 Convex programming · 90C47 Minimax problems

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Section: Simulation Results: Portfolio Optimizationmentioning

confidence: 99%

“…For large Wasserstein radii ε, the term λε dominates the objective function of problem (27). Using standard epi-convergence results [42,Section 7.E], one can thus show that…”

Section: Mean-risk Portfolio Optimizationmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable reformulations

2017

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“…Ambiguity sets of special interest include the Markov ambiguity set containing all distributions with known mean and support [48], the Chebyshev ambiguity set containing all distributions with known bounds on the first and second-order moments [12,14,22,31,39,46,49,51,52], the Gauss ambiguity set containing all unimodal distributions from within the Chebyshev ambiguity set [38,41], various generalized Chebyshev ambiguity sets that specify asymmetric moments [12,13,35], higher-order moments [7,30,45] or marginal moments [17,18], the median-absolute deviation ambiguity set containing all symmetric distributions with known median and mean absolute deviation [24], the Huber ambiguity set containing all distributions with known upper bound on the expected Huber loss function [15,48], the Wasserstein ambiguity set containing all distributions that are close to the empirical distribution with respect to the Wasserstein metric [19,34,40], the KullbackLeibler divergence ambiguity set and likelihood ratio ambiguity set [10,26,27,31,47] containing all distributions that are sufficiently likely to have generated a given data set, the Hoeffding ambiguity set containing all component-wise independent distributions with a box support [3,8,10], the Bernstein ambiguity set containing all distributions from within the Hoeffding ambiguity set subject to marginal moment bounds [36], several φ-divergence-based ambiguity sets [2,…”

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confidence: 99%

A distributionally robust perspective on uncertainty quantification and chance constrained programming

et al. 2015

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The objective of uncertainty quantification is to certify that a given physical, engineering or economic system satisfies multiple safety conditions with high probability. A more ambitious goal is to actively influence the system so as to guarantee and maintain its safety, a scenario which can be modeled through a chance constrained program. In this paper we assume that the parameters of the system are governed by an ambiguous distribution that is only known to belong to an ambiguity set characterized through generalized moment bounds and structural properties such as symmetry, unimodality or independence patterns. We delineate the watershed between tractability and intractability in ambiguity-averse uncertainty quantification and chance constrained programming. Using tools from distributionally robust optimization, we derive explicit conic reformulations for tractable problem classes and suggest efficiently computable conservative approximations for intractable ones.

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Data‐driven adaptive nested robust optimization: General modeling framework and efficient computational algorithm for decision making under uncertainty

2017

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A novel data‐driven adaptive robust optimization framework that leverages big data in process industries is proposed. A Bayesian nonparametric model—the Dirichlet process mixture model—is adopted and combined with a variational inference algorithm to extract the information embedded within uncertainty data. Further a data‐driven approach for defining uncertainty set is proposed. This machine‐learning model is seamlessly integrated with adaptive robust optimization approach through a novel four‐level optimization framework. This framework explicitly accounts for the correlation, asymmetry and multimode of uncertainty data, so it generates less conservative solutions. Additionally, the proposed framework is robust not only to parameter variations, but also to anomalous measurements. Because the resulting multilevel optimization problem cannot be solved directly by any off‐the‐shelf solvers, an efficient column‐and‐constraint generation algorithm is proposed to address the computational challenge. Two industrial applications on batch process scheduling and on process network planning are presented to demonstrate the advantages of the proposed modeling framework and effectiveness of the solution algorithm. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3790–3817, 2017

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Data-driven chance constrained stochastic program

Cited by 416 publications

References 46 publications

Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable reformulations

Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable reformulations

A distributionally robust perspective on uncertainty quantification and chance constrained programming

Data‐driven adaptive nested robust optimization: General modeling framework and efficient computational algorithm for decision making under uncertainty

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