AUTOSGM: A Unified Lowpass Regularization Framework for Accelerated Learning

This paper unifies commonly used accelerated stochastic gradient methods (Polyak’s Heavy Ball, Nesterov’s Accelerated Gradient and Adaptive Moment Estimation (Adam)) as specific cases of a general lowpass regularized learning framework, the Automatic Stochastic Gradient Method (AutoSGM). For AutoSGM, we derive an optimal iteration-dependent learning rate function and realize an approximation. Adam is also an approximation of this optimal approach that replaces the iteration-dependent learning-rate with a constant. Empirical results on deep neural networks comparing the learning behavior of AutoSGM equipped with this iteration-dependent learning-rate algorithm demonstrate fast learning behavior, robustness to the initial choice of the learning rate, and can tune an initial constant learning-rate in applications where a good constant learning rate approximation is unknown.