Stochastic Programming

A generalized Benders decomposition-based branch and cut algorithm for two-stage stochastic programs with nonconvex constraints and mixed-binary fi rst and second stage variables

  • Ignacio E. Grossmann
  • Can Li
    • Categories Stochastic Programming

    In this paper, we propose a generalized Benders decomposition-based branch and cut algorithm for solving two stage stochastic mixed-integer nonlinear programs (SMINLPs) with mixed binary rst and second stage variables. At a high level, the proposed decomposition algorithm performs spatial branch and bound search on the rst stage variables. Each node in the branch and … Read more

    On Data-Driven Prescriptive Analytics with Side Information: A Regularized Nadaraya-Watson Approach

  • Grani A. Hanasusanto
  • Chin Pang Ho
    • Categories Stochastic Programming

    We consider generic stochastic optimization problems in the presence of side information which enables a more insightful decision. The side information constitutes observable exogenous covariates that alter the conditional probability distribution of the random problem parameters. A decision maker who adapts her decisions according to the observed side information solves an optimization problem where the … Read more

    Admissibility of solution estimators for stochastic optimization

  • Amitabh Basu
  • Tu Nguyen
  • Ao Sun
    • Categories Stochastic Programming Tags , , ,

    We look at stochastic optimization problems through the lens of statistical decision theory. In particular, we address admissibility, in the statistical decision theory sense, of the natural sample average estimator for a stochastic optimization problem (which is also known as the empirical risk minimization (ERM) rule in learning literature). It is well known that for … Read more

    Zeroth-order Nonconvex Stochastic Optimization: Handling Constraints, High-Dimensionality, and Saddle-Points

  • Krishnakumar Balasubramanian
  • Saeed Ghadimi
    • Categories Nonlinear Optimization, Stochastic Programming Tags , , , , ,

    In this paper, we propose and analyze zeroth-order stochastic approximation algorithms for nonconvex and convex optimization, with a focus on addressing constrained optimization, high-dimensional setting, and saddle-point avoiding. To handle constrained optimization, we first propose generalizations of the conditional gradient algorithm achieving rates similar to the standard stochastic gradient algorithm using only zeroth-order information. To … Read more

    Two-stage Stochastic Programming with Linearly Bi-parameterized Quadratic Recourse

  • Ying Cui
  • Junyi Liu
  • Jong-Shi Pang
  • Suvrajeet Sen
    • Categories Stochastic Programming Tags , ,

    This paper studies the class of two-stage stochastic programs (SP) with a linearly bi-parameterized recourse function defined by a convex quadratic program. A distinguishing feature of this new class of stochastic programs is that the objective function in the second stage is linearly parameterized by the first-stage decision variable, in addition to the standard linear … Read more

    Distributionally Robust Optimization with Confidence Bands for Probability Density Functions

  • Xi Chen
  • Qihang Lin
  • Guanglin Xu
    • Categories Robust Optimization, Stochastic Programming

    Distributionally robust optimization (DRO) has been introduced for solving stochastic programs where the distribution of the random parameters is unknown and must be estimated by samples from that distribution. A key element of DRO is the construction of the ambiguity set, which is a set of distributions that covers the true distribution with a high … Read more

    Reinforcement Learning via Parametric Cost Function Approximation for Multistage Stochastic Programming

  • Saeed Ghadimi
  • Raymond Perkins
  • Warren B. Powell
    • Categories Applications - OR and Management Sciences, Optimization of Simulated Systems, Stochastic Programming Tags , , , ,

    The most common approaches for solving stochastic resource allocation problems in the research literature is to either use value functions (“dynamic programming”) or scenario trees (“stochastic programming”) to approximate the impact of a decision now on the future. By contrast, common industry practice is to use a deterministic approximation of the future which is easier … Read more

    A Single Time-Scale Stochastic Approximation Method for Nested Stochastic Optimization

  • Saeed Ghadimi
  • Andrzej Ruszczyński
  • Mengdi Wang
    • Categories Nonlinear Optimization, Stochastic Programming Tags , ,

    We study constrained nested stochastic optimization problems in which the objective function is a composition of two smooth functions whose exact values and derivatives are not available. We propose a single time-scale stochastic approximation algorithm, which we call the Nested Averaged Stochastic Approximation (NASA), to find an approximate stationary point of the problem. The algorithm … Read more

    A stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs

  • Rohit Kannan
  • James R. Luedtke
    • Categories Stochastic Programming Tags , , ,

    We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the efficient frontier of optimal objective value versus risk of constraint violation. To this end, we construct a reformulated problem whose objective is to minimize … Read more

    Machine learning approach to chance-constrained problems: An algorithm based on the stochastic gradient descent

  • Lukáš Adam
  • Martin Branda
    • Categories Stochastic Programming Tags , , , , ,

    We consider chance-constrained problems with discrete random distribution. We aim for problems with a large number of scenarios. We propose a novel method based on the stochastic gradient descent method which performs updates of the decision variable based only on looking at a few scenarios. We modify it to handle the non-separable objective. A complexity … Read more