distributionally robust optimization

On deterministic reformulations of distributionally robust joint chance constrained optimization problems

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

    A joint chance constrained optimization problem involves multiple uncertain constraints, i.e., constraints with stochastic parameters, that are jointly required to be satisfied with probability exceeding a prespecified threshold. In a distributionally robust joint chance constrained optimization problem (DRCCP), the joint chance constraint is required to hold for all probability distributions of the stochastic parameters from … Read more

    Closed-form solutions for worst-case law invariant risk measures with application to robust portfolio optimization

  • Jonathan Yu-Meng Li
    • Categories Applications - OR and Management Sciences, Robust Optimization Tags ,

    Worst-case risk measures refer to the calculation of the largest value for risk measures when only partial information of the underlying distribution is available. For the popular risk measures such as Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR), it is now known that their worst-case counterparts can be evaluated in closed form when only the first … Read more

    Distributionally Robust Optimization with Infinitely Constrained Ambiguity Sets

  • Melvyn Sim
  • Huan Xu
  • Zhi Chen
    • Categories Robust Optimization Tags ,

    We consider a distributionally robust optimization problem where the ambiguity set of probability distributions is characterized by a tractable conic representable support set and expectation constraints. Specifically, we propose and motivate a new class of infinitely constrained ambiguity sets in which the number of expectation constraints could potentially be infinite. We show how the infinitely … Read more

    Adjustable Robust Optimization via Fourier-Motzkin Elimination

  • Dick den Hertog
  • Melvyn Sim
  • Jianzhe Zhen
    • Categories Robust Optimization Tags , , ,

    We demonstrate how adjustable robust optimization (ARO) problems with fixed recourse can be casted as static robust optimization problems via Fourier-Motzkin elimination (FME). Through the lens of FME, we characterize the structures of the optimal decision rules for a broader class of ARO problems. A scheme based on a blending of classical FME and a … Read more

    Frechet inequalities via convex optimization

  • Paul Embrechts
  • Paul J. Goulart
  • Bart Paul Gerard Van Parys
    • Categories Convex Optimization, Infinite Dimensional Optimization, Robust Optimization Tags , ,

    Quantifying the risk carried by an aggregate position $S_d\defn\sum_{i=1}^d X_i$ comprising many risk factors $X_i$ is fundamental to both insurance and financial risk management. Frechet inequalities quantify the worst-case risk carried by the aggregate position given distributional information concerning its composing factors but without assuming independence. This marginal factor modeling of the aggregate position in … Read more

    Chebyshev Inequalities for Products of Random Variables

  • Daniel Kuhn
  • Napat Rujeerapaiboon
  • Wolfram Wiesemann
    • Categories Convex Optimization, Semi-definite Programming Tags , , ,

    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 numerically using semidefinite programming. If only an upper bound on the covariance matrix is available, … Read more

    Distributionally Robust Optimization with Principal Component Analysis

  • Richard Chen
  • Habib Najm
  • Jean-Paul Watson
  • Jianqiang Cheng
  • Ali Pinar
  • Cosmin Safta
    • Categories Robust Optimization, Stochastic Programming Tags , , ,

    Distributionally robust optimization (DRO) is widely used, because it offers a way to overcome the conservativeness of robust optimization without requiring the specificity of stochastic optimization. On the computational side, many practical DRO instances can be equivalently (or approximately) formulated as semidefinite programming (SDP) problems via conic duality of the moment problem. However, despite being … Read more

    Adaptive Distributionally Robust Optimization

  • Dimitris Bertsimas
  • Melvyn Sim
  • Meilin Zhang
    • Categories Robust Optimization Tags , ,

    We develop a modular and tractable framework for solving an adaptive distributionally robust linear opti- mization problem, where we minimize the worst-case expected cost over an ambiguity set of probability dis- tributions. The adaptive distrbutaionally robust optimization framework caters for dynamic decision making, where decisions can adapt to the uncertain outcomes as they unfold in … Read more

    Phi-Divergence Constrained Ambiguous Stochastic Programs for Data-Driven Optimization

  • Güzin Bayraksan
  • David Love
    • Categories Stochastic Programming Tags , , ,

    This paper investigates the use of phi-divergences in ambiguous (or distributionally robust) two-stage stochastic programs. Classical stochastic programming assumes the distribution of uncertain parameters are known. However, the true distribution is unknown in many applications. Especially in cases where there is little data or not much trust in the data, an ambiguity set of distributions … Read more

    Data-Driven Inverse Optimization with Imperfect Information

  • Grani A. Hanasusanto
  • Daniel Kuhn
  • Peyman Mohajerin Esfahani
  • Soroosh Shafieezadeh-Abadeh
    • Categories Linear, Cone and Semidefinite Programming, Robust Optimization, Stochastic Programming Tags , ,

    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 sequence of signals and corresponding optimal actions. We focus here on situations where the observer has imperfect … Read more