Residuals-based distributionally robust optimization with covariate information

Kannan, Rohit; Bayraksan, Güzi̇n; Luedtke, James

doi:10.48550/arxiv.2012.01088

Cited by 10 publications

(11 citation statements)

References 33 publications

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“…We devise a solution scheme for this variance regularized formulation based on a distri-butionally robust optimization (DRO) problem. Numerical results in the context of newsvendor and wind energy commitment problems demonstrate the superiority of our new regularized NW approximation over the linear decision rule scheme and a state-of-the-art DRO framework proposed by Kannan et al [2020b].…”

Section: Our Contributionsmentioning

confidence: 88%

“…With the idea of obtaining better out-of-sample performances on problems with limited data, the authors incorporate their residual-based formulation into a DRO framework [Kannan et al, 2020b] and also consider extensions where they relax the homoscedasticity assumption on the residuals [Kannan et al, 2021]. In a similar spirit, Elmachtoub and Grigas [2021] propose a smart "Predict, then Optimize" framework for contextual optimization problems with an unknown linear objective.…”

Section: Literature Reviewmentioning

confidence: 99%

“…We then benchmark our Regularized Nadaraya-Watson (RNW) method with sample average approximation (SAA), the unregularized Nadaraya-Watson (NW) [Hannah and Dunson, 2011] and the residual-based distributionally robust optimization (ERDRO) [Kannan et al, 2020b] methods in out-of-sample experiments. We also implemented the regularized linear decision rule (LDR) method [Bazier-Matte and Delage, 2020]; however, the method performs poorly and thus we do not report the results.…”

Section: Wind Energy Commitmentmentioning

confidence: 99%

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On Data-Driven Prescriptive Analytics with Side Information: A Regularized Nadaraya-Watson Approach

Srivastava¹,

Wang²,

Hanasusanto³

et al. 2021

Preprint

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We consider generic stochastic optimization problems in the presence of side information which enables a more insightful decision. The side information constitutes observable exogenous covariates that alter the conditional probability distribution of the random problem parameters. A decision maker who adapts her decisions according to the observed side information solves an optimization problem where the objective function is specified by the conditional expectation of the random cost. If the joint probability distribution is unknown, then the conditional expectation can be approximated in a data-driven manner using the Nadaraya-Watson (NW) kernel regression. While the emerging approximation scheme has found successful applications in diverse decision problems under uncertainty, it is largely unknown whether the scheme can provide any reasonable out-of-sample performance guarantees. In this paper, we establish guarantees for the generic problems by leveraging techniques from moderate deviations theory. Our analysis motivates the use of a variance-based regularization scheme which, in general, leads to a non-convex optimization problem. We adopt ideas from distributionally robust optimization to obtain tractable formulations. We present numerical experiments for newsvendor and wind energy commitment problems to highlight the effectiveness of our regularization scheme.

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Section: Our Contributionsmentioning

confidence: 88%

Section: Literature Reviewmentioning

confidence: 99%

Section: Wind Energy Commitmentmentioning

confidence: 99%

See 1 more Smart Citation

On Data-Driven Prescriptive Analytics with Side Information: A Regularized Nadaraya-Watson Approach

Srivastava¹,

Wang²,

Hanasusanto³

et al. 2021

Preprint

View full text Add to dashboard Cite

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“…For a concrete example, a portfolio allocation is usually based on historical data, and it is natural to evaluate the optimality gap of the portfolio selection conditional on the side information, for instance, based on market implied volatilities which reflect future market expectations. Several DRO formulations have been proposed recently to accommodate additional information; see, for example, [14,33,48,65], and this remains an emerging future direction for research.…”

Section: Conclusion and Final Considerationsmentioning

confidence: 99%

Statistical Analysis of Wasserstein Distributionally Robust Estimators

Blanchet¹,

Murthy²,

Nguyen³

2021

Preprint

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We consider statistical methods which invoke a min-max distributionally robust formulation to extract good out-of-sample performance in data-driven optimization and learning problems. Acknowledging the distributional uncertainty in learning from limited samples, the min-max formulations introduce an adversarial inner player to explore unseen covariate data. The resulting Distributionally Robust Optimization (DRO) formulations, which include Wasserstein DRO formulations (our main focus), are specified using optimal transportation phenomena. Upon describing how these infinite-dimensional min-max problems can be approached via a finite-dimensional dual reformulation, the tutorial moves into its main component, namely, explaining a generic recipe for optimally selecting the size of the adversary's budget. This is achieved by studying the limit behavior of an optimal transport projection formulation arising from an inquiry on the smallest confidence region that includes the unknown population risk minimizer. Incidentally, this systematic prescription coincides with those in specific examples in high-dimensional statistics and results in error bounds that are free from the curse of dimensions. Equipped with this prescription, we present a central limit theorem for the DRO estimator and provide a recipe for constructing compatible confidence regions that are useful for uncertainty quantification. The rest of the tutorial is devoted to insights into the nature of the optimizers selected by the min-max formulations and additional applications of optimal transport projections.

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“…Our framework is closely related to [25,26]. [26] construct the Wasserstein ambiguity set around the residuals, while ours is on the distribution of Y |X = x.…”

Section: Problemmentioning

confidence: 99%

Distributionally Robust Prescriptive Analytics with Wasserstein Distance

Wang¹,

Chen²,

Wang³

2021

Preprint

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In prescriptive analytics, the decision-maker observes historical samples of (X, Y ), where Y is the uncertain problem parameter and X is the concurrent covariate, without knowing the joint distribution. Given an additional covariate observation x, the goal is to choose a decision z conditional on this observation to minimize the cost E[c(z, Y )|X = x]. This paper proposes a new distributionally robust approach under Wasserstein ambiguity sets, in which the nominal distribution of Y |X = x is constructed based on the Nadaraya-Watson kernel estimator concerning the historical data. We show that the nominal distribution converges to the actual conditional distribution under the Wasserstein distance. We establish the out-ofsample guarantees and the computational tractability of the framework. Through synthetic and empirical experiments about the newsvendor problem and portfolio optimization, we demonstrate the strong performance and practical value of the proposed framework.Preprint. Under review.

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Residuals-based distributionally robust optimization with covariate information

Cited by 10 publications

References 33 publications

On Data-Driven Prescriptive Analytics with Side Information: A Regularized Nadaraya-Watson Approach

On Data-Driven Prescriptive Analytics with Side Information: A Regularized Nadaraya-Watson Approach

Statistical Analysis of Wasserstein Distributionally Robust Estimators

Distributionally Robust Prescriptive Analytics with Wasserstein Distance

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