distributionally robust optimization

Tractable Reformulations of Distributionally Robust Two-stage Stochastic Programs with $\infty- Distance

  • Weijun Xie
    • Categories Stochastic Programming Tags , , , ,

    This paper studies a two-stage distributionally robust stochastic linear program under the type-∞ Wasserstein ball by providing sufficient conditions under which the program can be efficiently computed via a tractable convex program. By exploring the properties of binary variables, the developed reformulation techniques are extended to those with mixed binary random parameters. The main tractable … Read more

    Distributionally robust chance constrained geometric optimization

  • Jia Liu
  • Abdel Lisser
  • Zhiping Chen
    • Categories Convex Optimization, Robust Optimization, Stochastic Programming Tags , , ,

    This paper discusses distributionally robust geometric programs with individual and joint chance constraints. Seven groups of uncertainty sets are considered: uncertainty sets with first two order moments information, uncertainty sets constrained by the Kullback-Leibler divergence distance with a normal reference distribution or a discrete reference distribution, uncertainty sets with known first moments or known first … Read more

    Tight tail probability bounds for distribution-free decision making

  • Ruud C.M. Brekelmans
  • Dick den Hertog
  • Wouter Van Eekelen
  • Ernst Roos
  • Johan Van Leeuwaarden
    • Categories Robust Optimization, Stochastic Programming Tags , , ,

    Chebyshev’s inequality provides an upper bound on the tail probability of a random variable based on its mean and variance. While tight, the inequality has been criticized for only being attained by pathological distributions that abuse the unboundedness of the underlying support and are not considered realistic in many applications. We provide alternative tight lower … Read more

    Distributionally Robust Partially Observable Markov Decision Process with Moment-based Ambiguity

  • Ruiwei Jiang
  • Siqian Shen
  • Hideaki Nakao
    • Categories Dynamic Programming, Robust Optimization Tags , , , ,

    We consider a distributionally robust Partially Observable Markov Decision Process (DR-POMDP), where the distribution of the transition-observation probabilities is unknown at the beginning of each decision period, but their realizations can be inferred using side information at the end of each period after an action being taken. We build an ambiguity set of the joint … Read more

    Confidence Regions in Wasserstein Distributionally Robust Estimation

  • Jose Blanchet
  • Karthyek Murthy
  • Nian Si
    • Categories Robust Optimization, Stochastic Programming Tags , , ,

    Wasserstein distributionally robust optimization (DRO) estimators are obtained as solutions of min-max problems in which the statistician selects a parameter minimizing the worst-case loss among all probability models within a certain distance (in a Wasserstein sense) from the underlying empirical measure. While motivated by the need to identify model parameters (or) decision choices that are … Read more

    Sharing the Value-at-Risk under Distributional Ambiguity

  • Weijun Xie
  • Zhi Chen
    • Categories Applications - OR and Management Sciences, Robust Optimization, Stochastic Programming Tags , , ,

    This paper considers the problem of risk sharing, where a coalition of homogeneous agents, each bearing a random cost, aggregates their costs and shares the value-at-risk of such a risky position. Due to limited distributional information in practice, the joint distribution of agents’ random costs is difficult to acquire. The coalition, being aware of the … Read more

    Distributionally robust optimization with multiple time scales: valuation of a thermal power plant

  • Daniela Escobar
  • Martin Glanzer
  • Georg Ch. Pflug
  • Wim van Ackooij
    • Categories Dynamic Programming, Stochastic Programming Tags , , , , , ,

    The valuation of a real option is preferably done with the inclusion of uncertainties in the model, since the value depends on future costs and revenues, which are not perfectly known today. The usual value of the option is defined as the maximal expected (discounted) profit one may achieve under optimal management of the operation. … Read more

    Discrete Approximation Scheme in Distributionally Robust Optimization

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

    Discrete approximation which is the prevailing scheme in stochastic programming in the past decade has been extended to distributionally robust optimization (DRO) recently. In this paper we conduct rigorous quantitative stability analysis of discrete approximation schemes for DRO, which measures the approximation error in terms of discretization sample size. For the ambiguity set defined through … Read more

    Decomposition Methods for Solving Two-Stage Distributionally Robust Optimization Problems

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

    Decomposition methods have been well studied for solving two-stage and multi-stage stochastic programming problems, see [29, 32, 33]. In this paper, we propose an algorithmic framework based on the fundamental ideas of the methods for solving two-stage minimax distributionally robust optimization (DRO) problems where the underlying random variables take a finite number of distinct values. … 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