A New Likelihood Ratio Method for Training Artificial Neural Networks

Yijie Peng, Li Xiao, Bernd Heidergott, L. Jeff Hong, Henry Lam

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

We investigate a new approach to compute the gradients of artificial neural networks (ANNs), based on the so-called push-out likelihood ratio method. Unlike the widely used backpropagation (BP) method that requires continuity of the loss function and the activation function, our approach bypasses this requirement by injecting artificial noises into the signals passed along the neurons. We show how this approach has a similar computational complexity as BP, and moreover is more advantageous in terms of removing the backward recursion and eliciting transparent formulas. We also formalize the connection between BP, a pivotal technique for training ANNs, and infinitesimal perturbation analysis, a classic path-wise derivative estimation approach, so that both our new proposed methods and BP can be better understood in the context of stochastic gradient estimation. Our approach allows efficient training for ANNs with more flexibility on the loss and activation functions, and shows empirical improvements on the robustness of ANNs under adversarial attacks and corruptions of natural noises. Summary of Contribution: Stochastic gradient estimation has been studied actively in simulation for decades and becomes more important in the era of machine learning and artificial intelligence. The stochastic gradient descent is a standard technique for training the artificial neural networks (ANNs), a pivotal problem in deep learning. The most popular stochastic gradient estimation technique is the backpropagation method. We find that the backpropagation method lies in the family of infinitesimal perturbation analysis, a path-wise gradient estimation technique in simulation. Moreover, we develop a new likelihood ratio-based method, another popular family of gradient estimation technique in simulation, for training more general ANNs, and demonstrate that the new training method can improve the robustness of the ANN.

Original languageEnglish (US)
Pages (from-to)638-655
Number of pages18
JournalINFORMS Journal on Computing
Volume34
Issue number1
DOIs
StatePublished - Jan 2022
Externally publishedYes

Bibliographical note

Publisher Copyright:
Copyright: © 2021 INFORMS.

Keywords

  • artificial neural network
  • image identification
  • stochastic gradient estimation

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