We develop a probabilistic machine learning method, which formulates a class of stochastic neural networks by a stochastic optimal control problem. An efficient stochastic gradient descent algorithm is introduced under the stochastic maximum principle framework. Convergence analysis for stochastic gradient descent optimization and numerical experiments for applications of stochastic neural networks are carried out to validate our methodology in both theory and performance.

中文翻译：

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随机最大原理在深度学习中的不确定性量化

我们开发了一种概率机器学习方法，该方法通过随机最优控制问题来表达一类随机神经网络。在随机最大原理框架下，引入了一种有效的随机梯度下降算法。进行了随机梯度下降优化的收敛性分析和随机神经网络应用的数值实验，以验证我们的方法论的理论和性能。