Robust Optimization

Distributionally robust second-order stochastic dominance constrained optimization with Wasserstein distance

  • Zhiping Chen
  • Jia Liu
  • Yu Mei
    • Categories Robust Optimization

    We consider a distributionally robust second-order stochastic dominance constrained optimization problem. We require the dominance constraints hold with respect to all probability distributions in a Wasserstein ball centered at the empirical distribution. We adopt the sample approximation approach to develop a linear programming formulation that provides a lower bound. We propose a novel split-and-dual decomposition … Read more

    Model-Free Assortment Pricing with Transaction Data

  • Ningyuan Chen
  • Andre Augusto Cire
  • Ming Hu
  • Saman Lagzi
    • Categories Applications - OR and Management Sciences, Approximation Algorithms, Robust Optimization

    We study a problem in which a firm sets prices for products based on the transaction data, i.e., which product past customers chose from an assortment and what were the historical prices that they observed. Our approach does not impose a model on the distribution of the customers’ valuations and only assumes, instead, that purchase … Read more

    The Landscape of the Proximal Point Method for Nonconvex-Nonconcave Minimax Optimization

  • Benjamin Grimmer
  • Haihao Lu
  • Vahab S. Mirrokni
  • Pratik Worah
    • Categories Robust Optimization, Unconstrained Optimization Tags , , , , , ,

    Minimax optimization has become a central tool for modern machine learning with applications in generative adversarial networks, robust optimization, reinforcement learning, etc. These applications are often nonconvex-nonconcave, but the existing theory is unable to identify and deal with the fundamental difficulties posed by nonconvex-nonconcave structures. In this paper, we study the classic proximal point method … Read more

    Data-Driven Optimization with Distributionally Robust Second-Order Stochastic Dominance Constraints

  • Chun Peng
  • Erick Delage
    • Categories Robust Optimization Tags , ,

    Optimization with stochastic dominance constraints has recently received an increasing amount of attention in the quantitative risk management literature. Instead of requiring that the probabilistic description of the uncertain parameters be exactly known, this paper presents the first comprehensive study of a data-driven formulation of the distributionally robust second-order stochastic dominance constrained problem (DRSSDCP) that … Read more

    Kernel Distributionally Robust Optimization

  • Moritz Diehl
  • Wittawat Jitkrittum
  • Bernhard Schölkopf
  • Jia-Jie Zhu
    • Categories Robust Optimization, Statistics, Stochastic Programming Tags , , ,

    We propose kernel distributionally robust optimization (Kernel DRO) using insights from the robust optimization theory and functional analysis. Our method uses reproducing kernel Hilbert spaces (RKHS) to construct a wide range of convex ambiguity sets, including sets based on integral probability metrics and finite-order moment bounds. This perspective unifies multiple existing robust and stochastic optimization … Read more

    Pareto Adaptive Robust Optimality via a Fourier-Motzkin Elimination Lens

  • Dimitris Bertsimas
  • Stefan ten Eikelder
  • Dick den Hertog
  • Nikolaos Trichakis
    • Categories Robust Optimization Tags , , , ,

    We formalize the concept of Pareto Adaptive Robust Optimality (PARO) for linear Adaptive Robust Optimization (ARO) problems. A worst-case optimal solution pair of here-and-now decisions and wait-and-see decisions is PARO if it cannot be Pareto dominated by another solution, i.e., there does not exist another such pair that performs at least as good in all … Read more

    Residuals-based distributionally robust optimization with covariate information

  • Rohit Kannan
  • Güzin Bayraksan
  • James R. Luedtke
    • Categories Robust Optimization, Stochastic Programming Tags , , , , , , ,

    We consider data-driven approaches that integrate a machine learning prediction model within distributionally robust optimization (DRO) given limited joint observations of uncertain parameters and covariates. Our framework is flexible in the sense that it can accommodate a variety of regression setups and DRO ambiguity sets. We investigate asymptotic and finite sample properties of solutions obtained … Read more

    Safely Learning Dynamical Systems from Short Trajectories

  • Amir Ali Ahmadi
  • Abraar Chaudhry
  • Vikas Sindhwani
  • Stephen Tu
    • Categories Control Applications, Linear, Cone and Semidefinite Programming, Robust Optimization Tags , , , ,

    A fundamental challenge in learning to control an unknown dynamical system is to reduce model uncertainty by making measurements while maintaining safety. In this work, we formulate a mathematical definition of what it means to safely learn a dynamical system by sequentially deciding where to initialize the next trajectory. In our framework, the state of … Read more

    Affine Decision Rule Approximation to Immunize against Demand Response Uncertainty in Smart Grids’ Capacity Planning

  • Sajad Aliakbari-Sani
  • Olivier Bahn
  • Erick Delage
    • Categories Energy, Linear Programming, Robust Optimization Tags , , ,

    Generation expansion planning (GEP) is a classical problem that determines an optimal investment plan for existing and future electricity generation technologies. GEP is a computationally challenging problem, as it typically corresponds to a very large-scale problem that contains several sources of uncertainties. With the advent of demand response (DR) as a reserved capacity in modern … Read more

    Stochastic Decomposition Method for Two-Stage Distributionally Robust Optimization

  • Manish Bansal
  • Harsha Gangammanavar
    • Categories Robust Optimization, Stochastic Programming

    In this paper, we present a sequential sampling-based algorithm for the two-stage distributionally robust linear programming (2-DRLP) models. The 2-DRLP models are defined over a general class of ambiguity sets with discrete or continuous probability distributions. The algorithm is a distributionally robust version of the well-known stochastic decomposition algorithm of Higle and Sen (Math. of … Read more