Daniel Kuhn

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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 distribut ...

2018

Data-Driven Inverse Optimization with Incomplete Information

Daniel Kuhn, Soroosh Shafieezadeh Abadeh, Peyman Mohajerin Esfahani, Grani Adiwena Hanasusanto

In data-driven inverse optimization an observer aims to learn the preferences of an agent who solves a parametric optimization problem depending on an exogenous signal. Thus, the observer seeks the agent's objective function that best explains a historical ...

2018

Chebyshev Inequalities for Products of Random Variables

Daniel Kuhn, Napat Rujeerapaiboon, Wolfram Wiesemann

We derive sharp probability bounds on the tails of a product of symmetric non-negative random variables using only information about their first two moments. If the covariance matrix of the random variables is known exactly, these bounds can be computed nu ...

2018

Ambiguous Joint Chance Constraints under Mean and Dispersion Information

Daniel Kuhn, Grani Adiwena Hanasusanto, Wolfram Wiesemann

We study joint chance constraints where the distribution of the uncertain parameters is only known to belong to an ambiguity set characterized by the mean and support of the uncertainties and by an upper bound on their dispersion. This setting gives rise t ...

Informs2017

Generalized Gauss Inequalities via Semidefinite Programming

Daniel Kuhn

A sharp upper bound on the probability of a random vector falling outside a polytope, based solely on the first and second moments of its distribution, can be computed efficiently using semidefinite programming. However, this Chebyshev-type bound tends to ...

Springer Verlag2016

Robust Growth-Optimal Portfolios

Daniel Kuhn, Napat Rujeerapaiboon, Wolfram Wiesemann

The growth-optimal portfolio is designed to have maximum expected log-return over the next rebalancing period. Thus, it can be computed with relative ease by solving a static optimization problem. The growth-optimal portfolio has sparked fascination among ...

Informs2016

A linear programming approach to the optimization of residential energy systems

Jan Van Herle, Daniel Kuhn, Dirk Lauinger, Priscilla Caliandro

A decision-support tool (ORES) in the form of a linear program is developed to determine the optimal investment and operating decisions for residential energy systems. It shows how energy conversion units such as a cogeneration fuel cell, a heat pump, a bo ...

2016

K-Adaptability in Two-Stage Distributionally Robust Binary Programming

Daniel Kuhn, Grani Adiwena Hanasusanto, Wolfram Wiesemann

We propose to approximate two-stage distributionally robust programs with binary recourse decisions by their associated K-adaptability problems, which pre-select K candidate second-stage policies here-and-now and implement the best of these policies once t ...

Elsevier Science Bv2016

Distributionally Robust Control of Constrained Stochastic Systems

Daniel Kuhn

We investigate the control of constrained stochastic linear systems when faced with only limited information regarding the disturbance process, i.e. when only the first two moments of the disturbance distribution are known. We consider two types of distrib ...

Institute of Electrical and Electronics Engineers2016

A Comment on “Computational Complexity of Stochastic Programming Problems”

Daniel Kuhn, Grani Adiwena Hanasusanto, Wolfram Wiesemann

Although stochastic programming problems were always believed to be computationally challenging, this perception has only recently received a theoretical justification by the seminal work of Dyer and Stougie (Mathematical Programming A, 106(3):423–432, 200 ...

Springer Heidelberg2016

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Data-Driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations

Daniel Kuhn, Peyman Mohajerin Esfahani

2018