The stochastic variance-reduced gradient method (SVRG) and its accelerated variant (Katyusha) have attracted enormous attention in the machine learning community in the last few years due to their superior theoretical properties and empirical behaviour on training supervised machine learning models via the empirical risk minimization paradigm. A key structural element in both of these methods is the inclusion of an outer loop at the beginning of which a full pass over the training data is made in order to compute the exact gradient, which is then used to construct a variance-reduced estimator of the gradient. In this work we design {\em loopless variants} of both of these methods. In particular, we remove the outer loop and replace its function by a coin flip performed in each iteration designed to trigger, with a small probability, the computation of the gradient. We prove that the new methods enjoy the same superior theoretical convergence properties as the original methods. However, we demonstrate through numerical experiments that our methods have substantially superior practical behavior.

本文设计了随机方差减少梯度方法（SVRG）和其加速变体（Katyusha）的无循环变体，证明了其在理论上具有与原始方法相同的卓越收敛性能，通过数值实验证明了这些方法在实践中具有显着优越性。

SVRG和Katyusha算法不需要外循环也能更优秀