Stochastic Programming

Strong Formulations for Distributionally Robust Chance-Constrained Programs with Left-Hand Side Uncertainty under Wasserstein Ambiguity

  • Nam Ho-Nguyen
  • Fatma Kılınç-Karzan
  • Simge Küçükyavuz
  • Dabeen Lee
    • Categories Robust Optimization, Stochastic Programming Tags , , , ,

    Distributionally robust chance-constrained programs (DR-CCP) over Wasserstein ambiguity sets exhibit attractive out-of-sample performance and admit big-$M$-based mixed-integer programming (MIP) reformulations with conic constraints. However, the resulting formulations often suffer from scalability issues as sample size increases. To address this shortcoming, we derive stronger formulations that scale well with respect to the sample size. Our focus … Read more

    Optimal design of an electricity-intensive industrial facility subject to electricity price uncertainty: stochastic optimization and scenario reduction

  • Adam R. Brandt
  • Holger Teichgraeber
    • Categories Chemical Engineering, Production and Logistics, Stochastic Programming Tags , , , ,

    When considering the design of electricity-intensive industrial processes, a challenge is that future electricity prices are highly uncertain. Design decisions made before construction can affect operations decades into the future. We thus explore whether including electricity price uncertainty into the design process affects design decisions. We apply stochastic optimization to the design and operations of … Read more

    Robust Spectral Risk Optimization When Information on Risk Spectrum Is Incomplete

  • Wei Wang
  • Huifu Xu
    • Categories Robust Optimization, Stochastic Programming Tags , , , ,

    Spectral risk measure (SRM) is a weighted average of value at risk (VaR) where the weighting function (also known as risk spectrum or distortion function) characterizes the decision maker’s risk attitude. In this paper, we consider the case where the decision maker’s risk spectrum is ambiguous and introduce a robust SRM model based on the … Read more

    Rates of convergence of sample average approximation under heavy tailed distributions

  • Zhiping Chen
  • Jie Jiang
  • Xinmin Yang
    • Categories Stochastic Programming

    In this paper, we consider the rate of convergence with sample average approximation (SAA) under heavy tailed distributions and quantify it under both independent identically distributed (iid) sampling and non-iid sampling. We rst derive the polynomial rate of convergence for random variable under iid sampling. Then, the uniform polynomial rates of convergence for both random … Read more

    An Analysis of Constant Step Size SGD in the Non-convex Regime: Asymptotic Normality and Bias

  • Krishnakumar Balasubramanian
  • Stanislav Volgushev
  • Murat A. Erdogdu
  • Lu Yu
    • Categories Statistics, Stochastic Approaches, Stochastic Programming Tags , ,

    Structured non-convex learning problems, for which critical points have favorable statistical properties, arise frequently in statistical machine learning. Algorithmic convergence and statistical estimation rates are well-understood for such problems. However, quantifying the uncertainty associated with the underlying training algorithm is not well-studied in the non-convex setting. In order to address this short-coming, in this work, … Read more

    Modeling Multi-stage Decision Making under Incomplete and Uncertain Information

  • Viktor Bindewald
  • Fabian Dunke
  • Stefan Nickel
    • Categories Applications - OR and Management Sciences, Robust Optimization, Stochastic Programming Tags , , , ,

    We propose a new universal framework for multi-stage decision making under limited information availability. It is developed as part of a larger research project which aims at providing analytical methods to compare and evaluate different models and algorithms for multi-stage decision making. In our setting, we have an open time horizon and limited information about … Read more

    Games with joint chance constraints under mixture distributions

  • Abdel Lisser
  • Shen Peng
  • Vikas Vikram Singh
  • Navnit Yadav
    • Categories Game Theory, Stochastic Programming Tags , ,

    We consider an n-player non-cooperative game where each player has expected value payoff function and her strategy set is defined by a joint chance constraint. The random constraint vectors are independent. We propose a subset of probability distributions from elliptical family of distributions. We consider the case when the probability distribution of each random constraint … Read more

    Equivalent second-order cone programs for distributionally robust zero-sum games

  • Ayush Agarwal
  • Abdel Lisser
  • Vikas Vikram Singh
  • Navnit Yadav
    • Categories Game Theory, Stochastic Programming Tags , , , ,

    We consider a two player zero-sum game with stochastic linear constraints. The probability distributions of the vectors associated with the constraints are partially known. The available information with respect to the distribution is based mainly on the two first moments. In this vein, we formulate the stochastic linear constraints as distributionally robust chance constraints. We … Read more

    Dual bounds for periodical stochastic programs

  • Yi Cheng
  • Alexander Shapiro
    • Categories Stochastic Programming Tags , , , , ,

    In this paper we discuss construction of the dual of a periodical formulation of infinite horizon linear stochastic programs with a discount factor. The dual problem is used for computing a deterministic upper bound for the optimal value of the considered multistage stochastic program. Numerical experiments demonstrate behavior of that upper bound especially when the … Read more

    Constant Depth Decision Rules for multistage optimization under uncertainty

  • Vincent Guigues
  • Anatoli Juditsky
  • Arkadi Nemirovski
    • Categories Stochastic Programming

    In this paper, we introduce a new class of decision rules, referred to as Constant Depth Decision Rules (CDDRs), for multistage optimization under linear constraints with uncertainty-affected right-hand sides. We consider two uncertainty classes: discrete uncertainties which can take at each stage at most a fixed number d of different values, and polytopic uncertainties which, … Read more