Rate of convergenceIn this paper we study the convergence properties of a Nesterov's family of inertial schemes which is a specific case of inertial Gradient Descent algorithm in the context of a smooth convex minimization problem, under some additional hypotheses on the local geometry of the ...
梯度下降(Gradient Descent)是一种简单且常用的优化方法,它可以被用来求解很多可导的凸优化问题(如逻辑回归,线性回归等)。同时,梯度下降在非凸优化问题的求解中也占有一席之地。我们常听到神经网络(neural network),也常常使用梯度下降及其变种(如随机梯度下降,Adam等)来最小化经验误差(empirical loss)。 不妨设可导的...
本文属于优化方向,基本的算法之一梯度下降法 (gradient descent, GD) 或者随机梯度下降法 (stochastic gradient descent, SGD) 的理论显示,对于一个 L -smooth 的连续目标函数,只要步长小于 2/L ,那么算法必定收敛,然而在实际应用中,步长往往并不满足该条件,但是算法仍然会收敛,尽管收敛的过程是不稳定的,或者说是...
On the other hand, if n is big, we can upgrade a few of coordinate per iteration, instead of updating the whole n dimension. This is Coordinate descent.For those problem where calculating coordinate gradient (i.e. partial derivative) is simple, it turns out the the rate for coordinate ...
They also presented a linear convergence rate of the vanilla Gradient Ascent Descent (GDA) method when the objective function f(x,y) is strongly convex-strongly concave.222Note that when we state that f(x,y) is strongly convex-strongly concave, it means that f(⋅,y) is strongly convex ...
With this stronger hypothesis, we derive estimates on the rate of convergence of to its limit. Using these results, we show that for functions satisfying the PL property, the convergence rate of both the objective function and the norm of the gradient with SGD is the same as the best-...
Using the gradient descent algorithm for designing a fuzzy estimator makes the tune of controller's parameters possible in different physical situations and uncertainties. Thanks to the voltage control strategy and fuzzy systems, there is no need for designers to have the knowledge of robots and ...
Recently, Yu and Guan proposed a modified PRP method (called DPRP method) which can generate sufficient descent directions for the objective function. They established the global convergence of the DPRP method based on the assumption that stepsize is bounded away from zero. In this paper, without...
Non-strongly-convex smooth stochastic approximation with convergence rate O(1/n). Advances in Neural Information Processing Systems, 2013.[12] MIkhail Belkin, Daniel Hsu, Siyuan Ma, Soumik Mandal. Reconciling modern machine-learning practice and the classical bias–variance trade-off. Proceedings of ...
On Projected Stochastic Gradient Descent Algorithm with Weighted Averaging for Least Squares Regression A stochastic gradient descent based algorithm with weighted iterate-averaging that uses a single pass over the data is studied and its convergence rate is ... K Cohen,A Nedic,R Srikant - 《IEEE ...