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This paper builds Wasserstein ambiguity sets for the unknown probability distribution of dynamic random variables leveraging noisy partial-state observations. The constructed ambiguity sets contain the true distribution of the data with quantifiable probability and can be exploited to formulate robust stochastic optimization problems with out-of-sample guarantees. We assume the random variable evolves in discrete time under uncertain initial conditions and dynamics, and that noisy partial measurements are available. All random elements have unknown probability distributions and we make inferences about the distribution of the state vector using several output samples from multiple realizations of the process. To this end, we leverage an observer to estimate the state of each independent realization and exploit the outcome to construct the ambiguity sets. We illustrate our results in an economic dispatch problem involving distributed energy resources over which the scheduler has no direct control., Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Team Dimitris Boskos

The aim of this paper is to compare two classes of structured ambiguity sets, which are data-driven and can reduce the conservativeness of their associated optimization problems. These two classes of structured sets, coined Wasserstein hyperrectangles and multi-transport hyperrectangles, are explored in their trade-offs in terms of reducing conservativeness and providing tractable reformulations. It follows that multi-transport hyperrectangles lead to tractable optimization problems for a significantly broader range of objective functions under a decent compromise in terms of conservativeness reduction. The results are illustrated in an uncertainty quantification case study., Accepted Author Manuscript, Team Dimitris Boskos, Team Jan-Willem van Wingerden

Ambiguity sets of probability distributions are a prominent tool to hedge against distributional uncertainty in stochastic optimization. The aim of this paper is to build tight Wasserstein ambiguity sets for data-driven optimization problems. The method exploits independence between the distribution components to introduce structure in the ambiguity sets and speed up their shrinkage with the number of collected samples. Tractable reformulations of the stochastic optimization problems are derived for costs that are expressed as sums or products of functions that depend only on the individual distribution components. The statistical benefits of the approach are theoretically analyzed for compactly supported distributions and demonstrated in a numerical example., Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Team Dimitris Boskos, Team Jan-Willem van Wingerden

This paper introduces a spectral parameterization of ambiguity sets to hedge against distributional uncertainty in stochastic optimization problems. We build an ambiguity set of probability densities around a histogram estimator, which is constructed by independent samples from the unknown distribution. The densities in the ambiguity set are determined by bounding the distance between the coefficients of their Haar wavelet expansion and the expansion of the histogram estimator. This representation facilitates the computation of expectations, leading to tractable minimax problems that are linear in the parameters of the ambiguity set, and enables the inclusion of additional constraints that can capture valuable prior information about the unknown distribution., Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Team Dimitris Boskos, Design for Sustainability