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Daniel Kuhn

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Related publications (69)

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Conic Programming Reformulations of Two-Stage Distributionally Robust Linear Programs over Wasserstein Balls

Daniel Kuhn, Grani Adiwena Hanasusanto

Adaptive robust optimization problems are usually solved approximately by restricting the adaptive decisions to simple parametric decision rules. However, the corresponding approximation error can be substantial. In this paper we show that two-stage robust ...

2018

On Risk Reduction in Kelly Betting Using the Conservative Expected Value

Daniel Kuhn, Napat Rujeerapaiboon

The celebrated Kelly betting strategy guarantees, with probability one, higher long-run wealth than any other causal investment strategy. However, on the way to its long-term supremacy, this strategy has a notable downfall: it typically displays high varia ...

2018

A Comment on “Computational Complexity of Stochastic Programming Problems”

Daniel Kuhn, Wolfram Wiesemann, Grani Adiwena Hanasusanto

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

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

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

Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning

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

Many decision problems in science, engineering and economics are affected by uncertain parameters whose distribution is only indirectly observable through samples. The goal of data-driven decision-making is to learn a decision from finitely many training s ...

2019

From Infinite to Finite Programs: Explicit Error Bounds with Applications to Approximate Dynamic Programming

Daniel Kuhn, John Lygeros, Peyman Mohajerin Esfahani, Tobias Sutter

We consider linear programming (LP) problems in infinite dimensional spaces that are in general computationally intractable. Under suitable assumptions, we develop an approximation bridge from the infinite-dimensional LP to tractable finite convex programs ...

SIAM Publications2018

Contextual Stochastic Bilevel Optimization

Daniel Kuhn, Andreas Krause, Yifan Hu

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

Energy and Reserve Dispatch with Distributionally Robust Joint Chance Constraints

Daniel Kuhn, Viet Anh Nguyen

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

Scenario Reduction Revisited: Fundamental Limits and Guarantees

Daniel Kuhn, Wolfram Wiesemann, Napat Rujeerapaiboon, Kilian Schindler

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

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

A Statistical Test for Probabilistic Fairness

Daniel Kuhn, Viet Anh Nguyen, 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

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

Distributionally Robust Convex Optimization

Daniel Kuhn, Wolfram Wiesemann

Distributionally robust optimization is a paradigm for decision-making under uncertainty where the uncertain problem data is governed by a probability distribution that is itself subject to uncertainty. The distribution is then assumed to belong to an ambi ...

2014

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

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

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

Sequential Domain Adaptation by Synthesizing Distributionally Robust Experts

Daniel Kuhn, Viet Anh Nguyen, 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

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

Reliable Frequency Regulation through Vehicle-to-Grid: Encoding Legislation with Robust Constraints

Daniel Kuhn, François Richard Vuille, Dirk Lauinger

Problem definition: Vehicle-to-grid increases the low utilization rate of privately owned electric vehicles by making their batteries available to electricity grids. We formulate a robust optimization problem that maximizes a vehicle owner’s expected profi ...

2024

Interdiction Games on Markovian PERT Networks

Daniel Kuhn, Wolfram Wiesemann

In a stochastic interdiction game a proliferator aims to minimize the expected duration of a nuclear weapons development project, and an interdictor endeavors to maximize the project duration by delaying some of the project tasks. We formulate static and d ...

Informs2015

Calculating Optimistic Likelihoods Using (Geodesically) Convex Optimization

Daniel Kuhn, Wolfram Wiesemann, Viet Anh Nguyen, Soroosh Shafieezadeh Abadeh

A fundamental problem arising in many areas of machine learning is the evaluation of the likelihood of a given observation under different nominal distributions. Frequently, these nominal distributions are themselves estimated from data, which makes them s ...

2019