sample average approximation

On the Out-of-Sample Performance of Stochastic Dynamic Programming and Model Predictive Control

  • Dominic S. T. Keehan
  • Andrew B. Philpott
  • Edward Anderson
    • Categories Dynamic Programming, Stochastic Programming Tags , , ,

    Sample average approximation-based stochastic dynamic programming (SDP) and model predictive control (MPC) are two different methods for approaching multistage stochastic optimization. In this paper we investigate the conditions under which SDP may be outperformed by MPC. We show that, depending on the presence of concavity or convexity, MPC can be interpreted as solving a mean-constrained … Read more

    Asymptotic Consistency for Nonconvex Risk-Averse Stochastic Optimization with Infinite Dimensional Decision Spaces

  • Johannes Milz
  • Thomas Surowiec
    • Categories Optimization of Systems modeled by PDEs, Stochastic Programming, Systems governed by Differential Equations Optimization Tags , , , , , , ,

    Optimal values and solutions of empirical approximations of stochastic optimization problems can be viewed as statistical estimators of their true values. From this perspective, it is important to understand the asymptotic behavior of these estimators as the sample size goes to infinity, which is both of theoretical as well as practical interest. This area of … Read more

    Monotonicity and Complexity of Multistage Stochastic Variational Inequalities

  • Jie Jiang
  • Hailin Sun
    • Categories Complementarity and Variational Inequalities, Stochastic Programming Tags , , ,

    In this paper, we consider multistage stochastic variational inequalities (MSVIs). First, we give multistage stochastic programs and multistage multi-player noncooperative game problems as source problems. After that, we derive the monotonicity properties of MSVIs under less restrictive conditions. Finally, the polynomial rate of convergence with respect to sample sizes between the original problem and its … Read more

    Spectral Projected Subgradient Method for Nonsmooth Convex Optimization Problems

  • Nataša Krejić
  • Nataša Krklec Jerinkić
  • Tijana Ostojić
    • Categories Constrained Nonlinear Optimization, Convex and Nonsmooth Optimization, Convex Optimization Tags , , , , ,

    We consider constrained optimization problems with a nonsmooth objective function in the form of mathematical expectation. The Sample Average Approximation (SAA) is used to estimate the objective function and variable sample size strategy is employed. The proposed algorithm combines an SAA subgradient with the spectral coefficient in order to provide a suitable direction which improves … Read more

    A Prescriptive Machine Learning Method for Courier Scheduling on Crowdsourced Delivery Platforms

  • Adam Behrendt
  • Martin Savelsbergh
  • He Wang
    • Categories Applications - OR and Management Sciences Tags , , ,

    Crowdsourced delivery platforms face the unique challenge of meeting dynamic customer demand using couriers not employed by the platform. As a result, the delivery capacity of the platform is uncertain. To reduce the uncertainty, the platform can offer a reward to couriers that agree to be available to make deliveries for a specified period of … Read more

    An inexact restoration-nonsmooth algorithm with variable accuracy for stochastic nonsmooth convex optimization problems in machine learning and stochastic linear complementarity problems

  • Nataša Krejić
  • Nataša Krklec Jerinkić
  • Tijana Ostojić
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization, Stochastic Programming Tags , , , ,

    We study unconstrained optimization problems with nonsmooth and convex objective function in the form of a mathematical expectation. The proposed method approximates the expected objective function with a sample average function using Inexact Restoration-based adapted sample sizes. The sample size is chosen in an adaptive manner based on Inexact Restoration. The algorithm uses line search … Read more

    Data-driven sample average approximation with covariate information

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

    We study optimization for data-driven decision-making when we have observations of the uncertain parameters within the optimization model together with concurrent observations of covariates. Given a new covariate observation, the goal is to choose a decision that minimizes the expected cost conditioned on this observation. We investigate three data-driven frameworks that integrate a machine learning … Read more

    On sample average approximation for two-stage stochastic programs without relatively complete recourse

  • Rui Chen
  • James R. Luedtke
    • Categories Stochastic Programming Tags , , ,

    We investigate sample average approximation (SAA) for two-stage stochastic programs without relatively complete recourse, i.e., for problems in which there are first-stage feasible solutions that are not guaranteed to have a feasible recourse action. As a feasibility measure of the SAA solution, we consider the “recourse likelihood”, which is the probability that the solution has … Read more

    Sample Average Approximation for Stochastic Nonconvex Mixed Integer Nonlinear Programming via Outer Approximation

  • David E. Bernal Neira
  • Kevin C Furman
  • Ignacio E. Grossmann
  • Can Li
    • Categories (Mixed) Integer Nonlinear Programming, Stochastic Programming Tags , , ,

    Stochastic mixed-integer nonlinear programming (MINLP) is a very challenging type of problem. Although there have been recent advances in developing decomposition algorithms to solve stochastic MINLPs, none of the existing algorithms can address stochastic MINLPs with continuous distributions. We propose a sample average approximation-based outer approximation algorithm (SAAOA) that can address nonconvex two-stage stochastic programs … Read more