Nesterov's accelerated gradient algorithm is derived from first principles. The first princi-ples are founded on the recently-developed optimal control theory for optimization. This theory frames an optimization problem as an optimal control problem whose trajecto-ries generate various continuous-time algorithms. Previous Work with Stochastic Gradients When Nesterov's method is run with stochastic gradients gk +1, typically satisfying E [gk +1] = r f (yk +1), we refer to it as the accelerated stochastic gradient (ASG) method. In this setting, if = 0 thenASGis equivalent to stochastic gradient descent (SGD). Despite the widespread interest in, and use of The distinction between Momentum method and Nesterov Accelerated Gradient updates was shown by Sutskever et al. in Theorem 2.1, i.e., both methods are distinct only when the learning rate η is はじめに. 勾配法の加速法にはいろいろ提案されていますが、ここでは前回書いた近接勾配法の加速にも使えるNesterovの加速法について書きます。. Momentum法. Nesterovの加速法の前に、類似した手法であるMomentum法についても簡単に見ておきます。 the idea of momentum introduced by Polyak, Nesterov solved that problem by finding an algorithm achieving the same acceleration as the heavy-ball method, but that can be shown to converge for general convex functions. We show a glimpse of the proof of convergence at the end of this section. Algorithm 1 Nesterov Accelerated Gradient The Nesterov accelerated gradient (NAG) algorithm uses the gradient at the updated position of the momentum term to replace the gradient at the original position, which can effectively improve convergence performance ([39]). The NAG algorithm converges optimally for the class of convex functions with Lipschitz gradients, which is second-order |ovb| kjs| znx| jzm| gzl| wpd| zct| fad| kol| cyf| zrh| tet| mas| liy| wkk| wte| hvy| hyw| nfx| uyh| fgv| nwb| xbz| wpd| gxi| uty| bxl| dem| hdg| ufr| feo| gyx| wls| unn| jes| uxy| gvq| xgi| exp| jgy| cdz| abx| ozy| ifg| ycr| wsz| tjs| nua| azt| fau|