SPI-Optimizer: An Integral-Separated PI Controller for Stochastic Optimization

To overcome the oscillation problem in the classical momentum-based optimizer, recent work associates it with the proportional-integral (PI) controller, and artificially adds D term producing a PID controller. It suppresses oscillation with the sacrifice of introducing extra hyper-parameter. In this paper, we analyze that the fluctuation problem relates to the lag effect of the integral (I) term, and propose SPI-Optimizer, an integral-Separated PI controller based optimizer WITHOUT introducing extra hyper-parameter. It separates momentum term adaptively when the inconsistency of current and historical gradient direction occurs. Extensive experiments demonstrate that SPI-Optimizer generalizes well on popular network architectures to eliminate the oscillation, and owns competitive performance with faster convergence speed (up to 40% epochs reduction ratio) and more accurate classification result on MNIST, CIFAR10, and CIFAR100 (up to 27.5% error reduction ratio) than state-of-the-art methods.