Daniel Kuhn

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

  • Dirk Lauinger
  • François Vuille
  • Daniel Kuhn
    • Categories Applications - OR and Management Sciences, Applications - Science and Engineering, Robust Optimization Tags , , , , ,

    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 profit from selling primary frequency regulation to the grid and guarantees that market commitments are met at all times for all frequency … Read more

    On Linear Optimization over Wasserstein Balls

  • Daniel Kuhn
  • Wolfram Wiesemann
  • Man-Chung Yue
    • Categories Robust Optimization, Stochastic Programming Tags , , , ,

    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 and solve data-driven optimization problems with rigorous statistical guarantees. In this technical note we prove that the Wasserstein ball is weakly compact under … Read more

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

  • Daniel Kuhn
  • Peyman Mohajerin Esfahani
  • Viet Anh Nguyen
  • Soroosh Shafieezadeh-Abadeh
    • Categories Infinite Dimensional Optimization, Statistics, Stochastic Programming Tags , ,

    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 an estimator—that is, a measurable function of the observation—and a fictitious adversary choosing a prior—that is, … Read more

    Optimistic Distributionally Robust Optimization for Nonparametric Likelihood Approximation

  • Daniel Kuhn
  • Viet Anh Nguyen
  • Soroosh Shafieezadeh-Abadeh
  • Wolfram Wiesemann
  • Man-Chung Yue
    • Categories Stochastic Programming Tags , , , ,

    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 that identifies a probability measure which lies in the neighborhood of the nominal measure and that maximizes the probability of observing … Read more

    Calculating Optimistic Likelihoods Using (Geodesically) Convex Optimization

  • Daniel Kuhn
  • Viet Anh Nguyen
  • Soroosh Shafieezadeh-Abadeh
  • Wolfram Wiesemann
  • Man-Chung Yue
    • Categories Generalized Convexity/Monoticity, Semi-definite Programming, Stochastic Programming Tags , , ,

    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 susceptible to estimation errors. We thus propose to replace each nominal distribution with an ambiguity set containing all distributions … Read more

    Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning

  • Daniel Kuhn
  • Peyman Mohajerin Esfahani
  • Viet Anh Nguyen
  • Soroosh Shafieezadeh-Abadeh
    • Categories Robust Optimization, Stochastic Programming

    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 samples that will perform well on unseen test samples. This learning task is difficult even if all training and test … Read more

    Energy and Reserve Dispatch with Distributionally Robust Joint Chance Constraints

  • Daniel Kuhn
  • Viet Anh Nguyen
  • Christos Ordoudis
  • Pierre Pinson
    • Categories Applications - Science and Engineering, Robust Optimization, Stochastic Programming Tags , , ,

    We develop a two-stage stochastic program for energy and reserve dispatch, which ensures the safe operation of a power system with a high penetration of renewables and a strong interdependence with the natural gas system. Distributionally robust joint chance constraints with Wasserstein ambiguity sets ensure that there is no need for load shedding and renewable … Read more

    Wasserstein Distributionally Robust Kalman Filtering

  • Daniel Kuhn
  • Peyman Mohajerin Esfahani
  • Viet Anh Nguyen
  • Soroosh Shafieezadeh-Abadeh
    • Categories Robust Optimization, Statistics, Stochastic Programming Tags , , ,

    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. Despite the non-convex nature of the ambiguity set, we prove that the estimation problem is equivalent to a tractable convex … Read more

    Robust Multidimensional Pricing: Separation without Regret

  • Çağıl Koçyiğit
  • Daniel Kuhn
  • Napat Rujeerapaiboon
    • Categories Robust Optimization Tags , , ,

    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 pricing problem as a zero-sum game between the seller, who chooses a selling … Read more

    Data-Driven Chance Constrained Programs over Wasserstein Balls

  • Zhi Chen
  • Daniel Kuhn
  • Wolfram Wiesemann
    • Categories (Mixed) Integer Nonlinear Programming, Robust Optimization, Stochastic Programming Tags , ,

    We provide an exact deterministic reformulation for data-driven chance constrained programs over Wasserstein balls. For individual chance constraints as well as joint chance constraints with right-hand side uncertainty, our reformulation amounts to a mixed-integer conic program. In the special case of a Wasserstein ball with the $1$-norm or the $\infty$-norm, the cone is the nonnegative … Read more