Stochastic Approximation approach to Stochastic Programming - Archive ouverte HAL Accéder directement au contenu
Rapport (Rapport De Recherche) Année : 2013

Stochastic Approximation approach to Stochastic Programming

Résumé

In this paper we consider optimization problems where the objective function is given in a form of the expectation. A basic difficulty of solving such stochastic optimization problems is that the involved multidimensional integrals (expectations) cannot be computed with high accuracy. The aim of this paper is to compare two computational approaches based on Monte Carlo sampling techniques, namely, the Stochastic Approximation (SA) and the Sample Average Approximation (SAA) methods. Both approaches, the SA and SAA methods, have a long history. Current opinion is that the SAA method can efficiently use a specific (say linear) structure of the considered problem, while the SA approach is a crude subgradient method which often performs poorly in practice. We intend to demonstrate that a properly modified SA approach can be competitive and even significantly outperform the SAA method for a certain class of convex stochastic problems. We extend the analysis to the case of convex-concave stochastic saddle point problems, and present (in our opinion highly encouraging) results of numerical experiments.
Fichier non déposé

Dates et versions

hal-00853911 , version 1 (24-08-2013)

Identifiants

  • HAL Id : hal-00853911 , version 1

Citer

Anatoli B. Juditsky, Guanghui Lan, Arkadii S. Nemirovski, Alexander Shapiro. Stochastic Approximation approach to Stochastic Programming. [Research Report] LJK. 2013. ⟨hal-00853911⟩
7751 Consultations
0 Téléchargements

Partager

Gmail Facebook X LinkedIn More