distributionally robust optimization

Distributionally robust optimization with polynomial densities: theory, models and algorithms

  • Etienne de Klerk
  • Daniel Kuhn
  • Krzysztof Postek
    • Categories Robust Optimization, Semi-definite Programming Tags , , ,

    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 of most existing distributionally robust optimization models is that their ambiguity sets contain pathological discrete distribution that give nature too much … Read more

    Data-DrivenWater Allocation under Climate Uncertainty: A Distributionally Robust Approach

  • Güzin Bayraksan
  • David Love
  • Jangho Park
    • Categories Civil and Environmental Engineering, Robust Optimization, Stochastic Programming Tags , , , ,

    This paper investigates the application of techniques from distributionally robust optimization (DRO) to water allocation under future uncertainty. Specifically, we look at a rapidly-developing area of Tucson, Arizona. Tucson, like many arid and semi-arid regions around the world, faces considerable uncertainty in its ability to provide water for its citizens in the future. The main … Read more

    Bootstrap Robust Prescriptive Analytics

  • Dimitris Bertsimas
  • Bart Paul Gerard Van Parys
    • Categories Convex Optimization, Robust Optimization, Statistics Tags , , , ,

    We address the problem of prescribing an optimal decision in a framework where its cost depends on uncertain problem parameters $Y$ that need to be learned from data. Earlier work by Bertsimas and Kallus (2014) transforms classical machine learning methods that merely predict $Y$ from supervised training data $[(x_1, y_1), \dots, (x_n, y_n)]$ into prescriptive … Read more

    Regularization via Mass Transportation

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

    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, overfitting is typically mitigated by adding regularization terms to the objective that penalize hypothesis complexity. In this paper … Read more

    Primal-Dual Hybrid Gradient Method for Distributionally Robust Optimization Problems

  • Yongchao Liu
  • Xiao-Ming Yuan
  • Shangzhi Zeng
  • Jin Zhang
    • Categories Robust Optimization Tags , , , ,

    We focus on the discretization approach to distributionally robust optimization (DRO) problems and propose a numerical scheme originated from the primal-dual hybrid gradient (PDHG) method that recently has been well studied in convex optimization area. Specifically, we consider the cases where the ambiguity set of the discretized DRO model is defined through the moment condition … Read more

    Distributionally robust simple integer recourse

  • Shabbir Ahmed
  • Weijun Xie
    • Categories Integer Programming, Robust Optimization, Stochastic Programming Tags , , , ,

    The simple integer recourse (SIR) function of a decision variable is the expectation of the integer round-up of the shortage/surplus between a random variable with a known distribution and the decision variable. It is the integer analogue of the simple (continuous) recourse function in two stage stochastic linear programming. Structural properties and approximations of SIR … Read more

    Discrete Approximation of Two-Stage Stochastic and Distributionally Robust Linear Complementarity Problems

  • Xiaojun Chen
  • Hailin Sun
  • Huifu Xu
    • Categories Robust Optimization, Stochastic Programming Tags , , , ,

    In this paper, we propose a discretization scheme for the two-stage stochastic linear complementarity problem (LCP) where the underlying random data are continuously distributed. Under some moderate conditions, we derive qualitative and quantitative convergence for the solutions obtained from solving the discretized two-stage stochastic LCP (SLCP). We ex- plain how the discretized two-stage SLCP may … Read more

    Robust Stochastic Optimization Made Easy with RSOME

  • Melvyn Sim
  • Peng Xiong
  • Zhi Chen
    • Categories Robust Optimization, Stochastic Programming Tags , ,

    We present a new distributionally robust optimization model called robust stochastic optimization (RSO), which unifies both scenario-tree based stochastic linear optimization and distributionally robust optimization in a practicable framework that can be solved using the state-of-the-art commercial optimization solvers. We also develop a new algebraic modeling package, RSOME to facilitate the implementation of RSO models. … Read more

    Distributionally Robust Markovian Traffic Equilibrium

  • Selin Damla Ahipasaoglu
  • Karthik Natarajan
  • Ugur Arikan
    • Categories Robust Optimization, Transportation Tags , ,

    Stochastic user equilibrium models are fundamental to the analysis of transportation systems. Such models are typically developed under the assumption of route based choice models for the users. A class of link based models under a Markovian assumption on the route choice behavior of the users has been proposed to deal with the drawbacks of … Read more

    Distributionally Robust Mechanism Design

  • Garud Iyengar
  • Çağıl Koçyiğit
  • Daniel Kuhn
  • Wolfram Wiesemann
    • Categories Robust Optimization Tags , , , ,

    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 vector governed by an ambiguous probability distribution, which belongs … Read more