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A simultaneous perturbation weak derivative estimator for stochastic neural networks

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  • Thomas Flynn

    (Brookhaven National Laboratory)

  • Felisa Vázquez-Abad

    (Hunter College)

Abstract

In this paper we study gradient estimation for a network of nonlinear stochastic units known as the Little model. Many machine learning systems can be described as networks of homogeneous units, and the Little model is of a particularly general form, which includes as special cases several popular machine learning architectures. However, since a closed form solution for the stationary distribution is not known, gradient methods which work for similar models such as the Boltzmann machine or sigmoid belief network cannot be used. To address this we introduce a method to calculate derivatives for this system based on measure-valued differentiation and simultaneous perturbation. This extends previous works in which gradient estimation algorithm’s were presented for networks with restrictive features like symmetry or acyclic connectivity.

Suggested Citation

  • Thomas Flynn & Felisa Vázquez-Abad, 2019. "A simultaneous perturbation weak derivative estimator for stochastic neural networks," Computational Management Science, Springer, vol. 16(4), pages 715-738, October.
    • Handle: RePEc:spr:comgts:v:16:y:2019:i:4:d:10.1007_s10287-019-00357-1
    DOI: 10.1007/s10287-019-00357-1
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    References listed on IDEAS

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    1. B. Heidergott & F. J. Vázquez-Abad, 2008. "Measure-Valued Differentiation for Markov Chains," Journal of Optimization Theory and Applications, Springer, vol. 136(2), pages 187-209, February.
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