Daniel Kuhn

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Efficient Learning of a Linear Dynamical System with Stability Guarantees

Daniel Kuhn, Tobias Sutter, Wouter Jongeneel

We propose a principled method for projecting an arbitrary square matrix to the non- convex set of asymptotically stable matrices. Leveraging ideas from large deviations theory, we show that this projection is optimal in an information-theoretic sense and ...

2023

A Unified Theory of Robust and Distributionally Robust Optimization via the Primal-Worst-Equals-Dual-Best Principle

Daniel Kuhn, Jianzhe Zhen, Wolfram Wiesemann

Robust and distributionally robust optimization are modeling paradigms for decision-making under uncertainty where the uncertain parameters are only known to reside in an uncertainty set or are governed by any probability distribution from within an ambigu ...

2023

Stability Verification of Neural Network Controllers using Mixed-Integer Programming

Colin Neil Jones, Daniel Kuhn, Roland Schwan

We propose a framework for the stability verification of Mixed-Integer Linear Programming (MILP) representable control policies. This framework compares a fixed candidate policy, which admits an efficient parameterization and can be evaluated at a low comp ...

2023

Dataset for the article "Frequency regulation with storage: On losses and profits"

Daniel Kuhn, François Richard Vuille, Dirk Lauinger

This dataset complements the article "Frequency regulation with storage: On losses and profits" by Dirk Lauinger, François Vuille, and Daniel Kuhn, available at https://arxiv.org/abs/2306.02987. The dataset contains the following files: 1.

Zenodo2023

Topological Linear System Identification via Moderate Deviations Theory

Daniel Kuhn, Tobias Sutter, Wouter Jongeneel

Two dynamical systems are topologically equivalent when their phase-portraits can be morphed into each other by a homeomorphic coordinate transformation on the state space. The induced equivalence classes capture qualitative properties such as stability or ...

2022

Robust Multidimensional Pricing: Separation without Regret

Daniel Kuhn, Napat Rujeerapaiboon, Cagil Kocyigit

We study a robust monopoly pricing problem with a minimax regret objective, where a seller endeavors to sell multiple goods to a single buyer, only knowing that the buyer's values for the goods range over a rectangular uncertainty set. We interpret this pr ...

2022

Distributionally Robust Inverse Covariance Estimation: The Wasserstein Shrinkage Estimator

Daniel Kuhn, Viet Anh Nguyen, Peyman Mohajerin Esfahani

We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a p-dimensional Gaussian random vector from n independent samples. The proposed model minimizes the worst ...

2022

On Linear Optimization over Wasserstein Balls

Daniel Kuhn, Wolfram Wiesemann

Wasserstein balls, which contain all probability measures within a pre-specified Wasserstein distance to a reference measure, have recently enjoyed wide popularity in the distributionally robust optimization and machine learning communities to formulate an ...

2022

Scenario Reduction Revisited: Fundamental Limits and Guarantees

Daniel Kuhn, Napat Rujeerapaiboon, Kilian Schindler, Wolfram Wiesemann

The goal of scenario reduction is to approximate a given discrete distribution with another discrete distribution that has fewer atoms. We distinguish continuous scenario reduction, where the new atoms may be chosen freely, and discrete scenario reduction, ...

2022

On Topological Equivalence in Linear Quadratic Optimal Control

Daniel Kuhn, Wouter Jongeneel

Dynamical systems are topologically equivalent when their orbits can be mapped onto each other via a homeomorphic change of coordinates. We will show that in general, closed-loop systems resulting from Linear Quadratic Optimal Control problems are all topo ...

2021

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