Finite dimensional approximation and Newton-based algorithm for stochastic approximation in Hilbert space

Kulkarni, Ankur A. ; Borkar, Vivek S. (2009) Finite dimensional approximation and Newton-based algorithm for stochastic approximation in Hilbert space Automatica, 45 (12). pp. 2815-2822. ISSN 0005-1098

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Official URL: http://www.sciencedirect.com/science/article/pii/S...

Related URL: http://dx.doi.org/10.1016/j.automatica.2009.09.031

Abstract

This paper presents a finite dimensional approach to stochastic approximation in infinite dimensional Hilbert space. The problem was motivated by applications in the field of stochastic programming wherein we minimize a convex function defined on a Hilbert space. We define a finite dimensional approximation to the Hilbert space minimizer. A justification is provided for this finite dimensional approximation. Estimates of the dimensionality needed are also provided. The algorithm presented is a two time-scale Newton-based stochastic approximation scheme that lives in this finite dimensional space. Since the finite dimensional problem can be prohibitively large dimensional, we operate our Newton scheme in a projected, randomly chosen smaller dimensional subspace.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Stochastic Approximation; Hilbert Spaces; Stochastic Programming; Convex Optimization; Random Projection
ID Code:81473
Deposited On:07 Feb 2012 05:01
Last Modified:07 Feb 2012 05:01

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