Daniel Kuhn

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Publications associées (69)

A Pareto Dominance Principle for Data-Driven Optimization

Daniel Kuhn, Tobias Sutter

We propose a statistically optimal approach to construct data-driven decisions for stochastic optimization problems. Fundamentally, a data-driven decision is simply a function that maps the available training data to a feasible action. It can always be exp ...

2024

Frequency Regulation with Storage: On Losses and Profits

Daniel Kuhn, François Richard Vuille, Dirk Lauinger

Low-carbon societies will need to store vast amounts of electricity to balance intermittent generation from wind and solar energy, for example, through frequency regulation. Here, we derive an analytical solution to the decision-making problem of storage o ...

2024

End-to-End Learning for Stochastic Optimization: A Bayesian Perspective

Daniel Kuhn, Tobias Sutter, Yves Rychener

We develop a principled approach to end-to-end learning in stochastic optimization. First, we show that the standard end-to-end learning algorithm admits a Bayesian interpretation and trains a posterior Bayes action map. Building on the insights of this an ...

2023

Bridging Bayesian and Minimax Mean Square Error Estimation via Wasserstein Distributionally Robust Optimization

Daniel Kuhn, Viet Anh Nguyen, Soroosh Shafieezadeh Abadeh, Peyman Mohajerin Esfahani

We introduce a distributionally robust minimium mean square error estimation model with a Wasserstein ambiguity set to recover an unknown signal from a noisy observation. The proposed model can be viewed as a zero-sum game between a statistician choosing a ...

2023

Semi-Discrete Optimal Transport: Hardness, Regularization and Numerical Solution

Daniel Kuhn, Soroosh Shafieezadeh Abadeh, Bahar Taskesen

Semi-discrete optimal transport problems, which evaluate the Wasserstein distance between a discrete and a generic (possibly non-discrete) probability measure, are believed to be computationally hard. Even though such problems are ubiquitous in statistics, ...

2023

On Approximations of Data-Driven Chance Constrained Programs over Wasserstein Balls

Daniel Kuhn, Zhi Chen, Wolfram Wiesemann

Distributionally robust chance constrained programs minimize a deterministic cost function subject to the satisfaction of one or more safety conditions with high probability, given that the probability distribution of the uncertain problem parameters affec ...

2023

PIQP: A Proximal Interior-Point Quadratic Programming Solver

Colin Neil Jones, Daniel Kuhn, Yuning Jiang, Roland Schwan

This paper presents PIQP, a high-performance toolkit for solving generic sparse quadratic programs (QP). Combining an infeasible Interior Point Method (IPM) with the Proximal Method of Multipliers (PMM), the algorithm can handle ill-conditioned convex QP p ...

IEEE2023

Discrete Optimal Transport with Independent Marginals is #P-Hard

Daniel Kuhn, Soroosh Shafieezadeh Abadeh, Bahar Taskesen

We study the computational complexity of the optimal transport problem that evaluates the Wasser- stein distance between the distributions of two K-dimensional discrete random vectors. The best known algorithms for this problem run in polynomial time in th ...

2023

Contextual Stochastic Bilevel Optimization

Daniel Kuhn, Yifan Hu, Andreas Krause, Jie Wang

We introduce contextual stochastic bilevel optimization (CSBO) -- a stochastic bilevel optimization framework with the lower-level problem minimizing an expectation conditioned on some contextual information and the upper-level decision variable. This fram ...

2023

Distributionally Robust Linear Quadratic Control

Daniel Kuhn, Bahar Taskesen, Cagil Kocyigit

Linear-Quadratic-Gaussian (LQG) control is a fundamental control paradigm that is studied in various fields such as engineering, computer science, economics, and neuroscience. It involves controlling a system with linear dynamics and imperfect observations ...

2023

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