distributionally robust optimization

Data-Driven Distributionally Preference Robust Optimization Models Based on Random Utility Representation in Multi-Attribute Decision Making

  • Jian Hu
  • Huifu Xu
  • Dali Zhang
    • Categories Robust Optimization, Stochastic Programming Tags , , ,

    Preference robust optimization (PRO) has recently been studied to deal with utility based decision making problems under ambiguity in the characterization of the decision maker’s (DM) preference. In this paper, we propose a novel PRO modeling paradigm which combines the stochastic utility theory with distributionally robust optimization technique. Based on the stochastic utility theory, our … Read more

    Distributionally Robust Fair Transit Resource Allocation During a Pandemic

  • Luying Sun
  • Weijun Xie
  • Tim Witten
    • Categories Applications - OR and Management Sciences Tags , , ,

    This paper studies Distributionally robust Fair transit Resource Allocation model (DrFRAM) under Wasserstein ambiguity set to optimize the public transit resource allocation during a pandemic. We show that the proposed DrFRAM is highly nonconvex and nonlinear and is, in general, NP-hard. Fortunately, we show that DrFRAM can be reformulated as a mixed-integer linear programming (MILP) … Read more

    Adjustable Distributionally Robust Optimization with Infinitely Constrained Ambiguity Sets

  • Haolin Ruan
  • Zhi Chen
  • Chin Pang Ho
    • Categories Robust Optimization Tags , , ,

    We study adjustable distributionally robust optimization problems where their ambiguity sets can potentially encompass an infinite number of expectation constraints. Although such an ambiguity set has great modeling flexibility in characterizing uncertain probability distributions, the corresponding adjustable problems remain computationally intractable and challenging. To overcome this issue, we propose a greedy improvement procedure that consists … Read more

    RSOME in Python: An Open-Source Package for Robust Stochastic Optimization Made Easy

  • Peng Xiong
  • Zhi Chen
    • Categories Modeling Languages and Systems, Robust Optimization Tags , , ,

    We develop a Python package called RSOME for modeling a wide spectrum of robust and distributionally robust optimization problems. RSOME serves as a modeling platform for formulating various optimization problems subject to distributional ambiguity in a highly readable and mathematically intuitive manner. Compared with the MATLAB version, RSOME in Python is more versatile and well … Read more

    Distributionally Robust Optimization with Markovian Data

  • Daniel Kuhn
  • Tobias Sutter
  • Mengmeng Li
    • Categories Robust Optimization, Stochastic Programming Tags , , ,

    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 distributionally robust optimization model to estimate the problem’s objective function and optimal solution. By leveraging results from … Read more

    Robust Generalization despite Distribution Shift via Minimum Discriminating Information

  • Andreas Krause
  • Daniel Kuhn
  • Tobias Sutter
    • Categories Robust Optimization Tags , , , , ,

    Training models that perform well under distribution shifts is a central challenge in machine learning. In this paper, we introduce a modeling framework where, in addition to training data, we have partial structural knowledge of the shifted test distribution. We employ the principle of minimum discriminating information to embed the available prior knowledge, and use … Read more

    On the Optimality of Affine Decision Rules in Robust and Distributionally Robust Optimization

  • Angelos Georghiou
  • Angelos Tsoukalas
  • Wolfram Wiesemann
    • Categories Robust Optimization Tags ,

    We propose tight conditions under which two-stage robust and distributionally robust optimization problems are optimally solved in affine decision rules. Contrary to previous work, our conditions do not impose any structure on the support of the uncertain problem parameters, and they ensure point-wise (as opposed to worst-case) optimality of affine decision rules. The absence of … Read more

    Mathematical Foundations of Robust and Distributionally Robust Optimization

  • Daniel Kuhn
  • Wolfram Wiesemann
  • Jianzhe Zhen
    • Categories Robust Optimization Tags , ,

    Robust and distributionally robust optimization are modeling paradigms for decision-making under uncertainty where the uncertain parameters are only known to reside in an uncertainty set or are governed by any probability distribution from within an ambiguity set, respectively, and a decision is sought that minimizes a cost function under the most adverse outcome of the … Read more

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

  • Bahar TaČ™kesen
  • Soroosh Shafieezadeh-Abadeh
  • Daniel Kuhn
    • Categories Convex and Nonsmooth Optimization, Robust Optimization, Stochastic Programming Tags , , , , , ,

    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, machine learning and computer vision, however, this perception has not yet received a theoretical justification. To fill this gap, we prove that … Read more

    Robust and Distributionally Robust Optimization Models for Support Vector Machine

  • Daniel Faccini
  • Francesca Maggioni
  • Florian A. Potra
    • Categories Applications - OR and Management Sciences, Robust Optimization Tags , , , ,

    In this paper we present novel data-driven optimization models for Support Vector Machines (SVM), with the aim of linearly separating two sets of points that have non-disjoint convex closures. Traditional classi cation algorithms assume that the training data points are always known exactly. However, real-life data are often subject to noise. To handle such uncertainty, we … Read more