Stochastic Modified Equations and Adaptive Stochastic Gradient Algorithms


Qianxiao Li, Cheng Tai, Weinan E ;
Proceedings of the 34th International Conference on Machine Learning, PMLR 70:2101-2110, 2017.


We develop the method of stochastic modified equations (SME), in which stochastic gradient algorithms are approximated in the weak sense by continuous-time stochastic differential equations. We exploit the continuous formulation together with optimal control theory to derive novel adaptive hyper-parameter adjustment policies. Our algorithms have competitive performance with the added benefit of being robust to varying models and datasets. This provides a general methodology for the analysis and design of stochastic gradient algorithms.

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