On Sample Size Control in Sample Average Approximations for Solving Smooth Stochastic Programs

Abstract

We consider smooth stochastic programs and develop a discrete-time optimal-control problem for adaptively selecting sample sizes in a class of algorithms based on sample average approximations (SAA). The control problem aims to minimize the expected computational cost to obtain a near-optimal solution of a stochastic program and is solved approximately using dynamic programming. The optimal-control problem depends on unknown parameters such as rate of convergence, computational cost per iteration, and sampling error. Hence, we implement the approach within a receding-horizon framework where parameters are estimated and the optimal- control problem is solved repeatedly during the calculations of a SAA algorithm. The resulting sample-size selection policy consistently produces near-optimal solutions in short computing times as compared to other plausible policies in several numerical examples.

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Document Details

Document Type
Technical Report
Publication Date
Dec 21, 2009
Accession Number
ADA513136

Entities

People

  • Johannes Ø. Røyset

Organizations

  • Naval Postgraduate School

Tags

Communities of Interest

  • Engineered Resilient Systems
  • Human Systems

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Computer Programming
  • Computers
  • Distribution Functions
  • Equations
  • Mathematical Programming
  • Nonlinear Programming
  • Normal Distribution
  • Operating Systems
  • Operations Research
  • Optimization
  • Probability
  • Probability Distributions
  • Random Variables
  • Sampling
  • Standards

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Operations Research
  • Statistical inference.