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Daniel Kuhn

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Publications associées (69)

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, Wolfram Wiesemann, Jianzhe Zhen

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"

François Richard Vuille, Dirk Lauinger, Daniel Kuhn

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

Peyman Mohajerin Esfahani, Viet Anh Nguyen, Daniel Kuhn

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

A Statistical Test for Probabilistic Fairness

Viet Anh Nguyen, Daniel Kuhn, Bahar Taskesen

Algorithms are now routinely used to make consequential decisions that affect human lives. Examples include college admissions, medical interventions or law enforcement. While algorithms empower us to harness all information hidden in vast amounts of data, ...

2021

Sequential Domain Adaptation by Synthesizing Distributionally Robust Experts

Viet Anh Nguyen, Daniel Kuhn, Bahar Taskesen

Least squares estimators, when trained on a few target domain samples, may predict poorly. Supervised domain adaptation aims to improve the predictive accuracy by exploiting additional labeled training samples from a source distribution that is close to th ...

JMLR-JOURNAL MACHINE LEARNING RESEARCH2021

Distributionally Robust Optimization with Markovian Data

Daniel Kuhn, Tobias Sutter, Mengmeng Li

We study a stochastic program where the probability distribution of the uncertain problem parameters is unknown and only indirectly observed via finitely many correlated samples generated by an unknown Markov chain with d states. We propose a data-driven d ...

JMLR-JOURNAL MACHINE LEARNING RESEARCH2021

Energy and Reserve Dispatch with Distributionally Robust Joint Chance Constraints

Christos Ordoudis, Viet Anh Nguyen, Daniel Kuhn

We develop a two-stage stochastic program for energy and reserve dispatch of a joint power and gas system with a high penetration of renewables. Data-driven distributionally robust chance constraints ensure that there is no load shedding and renewable spil ...

2021

Robust Generalization despite Distribution Shift via Minimum Discriminating Information

Daniel Kuhn, Tobias Sutter, Andreas Krause

Training models that perform well under distribution shifts is a central challenge in machine learning. In this paper, we introduce a modeling framework where, in addition to training data, we have partial structural knowledge of the shifted test distribut ...

2021

From Data to Decisions: Distributionally Robust Optimization is Optimal

Peyman Mohajerin Esfahani, Daniel Kuhn

We study stochastic programs where the decision-maker cannot observe the distribution of the exogenous uncertainties but has access to a finite set of independent samples from this distribution. In this setting, the goal is to find a procedure that transfo ...

2021

Distributionally Robust Optimization with Polynomial Densities: Theory, Models and Algorithms

Daniel Kuhn

In distributionally robust optimization the probability distribution of the uncertain problem parameters is itself uncertain, and a fictitious adversary, e.g., nature, chooses the worst distribution from within a known ambiguity set. A common shortcoming o ...

2020

Distributionally Robust Mechanism Design

Daniel Kuhn, Cagil Kocyigit, Wolfram Wiesemann

We study a mechanism design problem where an indivisible good is auctioned to multiple bidders, for each of whom it has a private value that is unknown to the seller and the other bidders. The agents perceive the ensemble of all bidder values as a random v ...

2020

The Decision Rule Approach to Optimisation under Uncertainty: Methodology and Applications

Daniel Kuhn, Wolfram Wiesemann

Dynamic decision-making under uncertainty has a long and distinguished history in operations research. Due to the curse of dimensionality, solution schemes that naively partition or discretize the support of the random problem parameters are limited to sma ...

2019

"Dice"-sion Making under Uncertainty: When Can a Random Decision Reduce Risk?

Daniel Kuhn, Wolfram Wiesemann

Stochastic programming and distributionally robust optimization seek deterministic decisions that optimize a risk measure, possibly in view of the most adverse distribution in an ambiguity set. We investigate under which circumstances such deterministic de ...

2019

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