A New Likelihood Ratio Method for Training Artificial Neural Networks

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

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

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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
Pages (from-to)638-655
Number of pages18
JournalINFORMS Journal on Computing
Issue number1
Early online date17 Sept 2021
Publication statusPublished - Feb 2022

Bibliographical note

Funding Information:
History: Accepted by Bruno Tuffin, Area Editor for Simulation. Funding: This work was supported by the National Natural Science Foundation of China [Grants 71901003 and 72022001], National Science Foundation [Grants MMI-1834710 and IIS-1849280], and CAS Pioneer Hundred Talents Program [Grant 2017-074]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/ijoc.2021.1088.

Publisher Copyright:
Copyright: © 2021 INFORMS.


  • artificial neural network
  • image identification
  • stochastic gradient estimation


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