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Daniel Kuhn

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Publications associées (69)

Regularization via Mass Transportation

Peyman Mohajerin Esfahani, Daniel Kuhn, Soroosh Shafieezadeh Abadeh

The goal of regression and classification methods in supervised learning is to minimize the empirical risk, that is, the expectation of some loss function quantifying the prediction error under the empirical distribution. When facing scarce training data, ...

2019

Calculating Optimistic Likelihoods Using (Geodesically) Convex Optimization

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

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

Optimistic Distributionally Robust Optimization for Nonparametric Likelihood Approximation

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

The likelihood function is a fundamental component in Bayesian statistics. However, evaluating the likelihood of an observation is computationally intractable in many applications. In this paper, we propose a non-parametric approximation of the likelihood ...

2019

Size Matters: Cardinality-Constrained Clustering and Outlier Detection via Conic Optimization

Daniel Kuhn, Napat Rujeerapaiboon, Kilian Schindler, Wolfram Wiesemann

Plain vanilla K-means clustering is prone to produce unbalanced clusters and suffers from outlier sensitivity. To mitigate both shortcomings, we formulate a joint outlier-detection and clustering problem, which assigns a prescribed number of datapoints to ...

2019

Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning

Peyman Mohajerin Esfahani, Viet Anh Nguyen, Daniel Kuhn, 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

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

Decision Rule Bounds for Two-Stage Stochastic Bilevel Programs

Daniel Kuhn

We study stochastic bilevel programs where the leader chooses a binary here-and-now decision and the follower responds with a continuous wait-and-see-decision. Using modern decision rule approximations, we construct lower bounds on an optimistic version an ...

2018

Wasserstein Distributionally Robust Kalman Filtering

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

We study a distributionally robust mean square error estimation problem over a nonconvex Wasserstein ambiguity set containing only normal distributions. We show that the optimal estimator and the least favorable distribution form a Nash equilibrium. Despit ...

2018

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

Peyman Mohajerin Esfahani, Daniel Kuhn, John Lygeros, 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 ...

2018

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

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

Peyman Mohajerin Esfahani, Daniel Kuhn

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

Peyman Mohajerin Esfahani, Daniel Kuhn, Soroosh Shafieezadeh Abadeh, 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, Dirk Lauinger, Priscilla Caliandro, Daniel Kuhn

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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