我们用来自真实分析的思想补充这些见解,以进一步激发投影梯度下降(PGD)作为通用的“一阶攻击”,即,利用有关网络的本地一阶信息的最强攻击。 我们探索了网络架构对对抗鲁棒性的影响,并发现模型能力在这里起着重要的作用。为了可靠地抵抗强大的对抗攻击,网络需要的容量要比仅正确分类良性样本的容量更大。这表明,鞍点问题的鲁棒决策边界比仅将良性
投影梯度下降是梯度下降的一种变形,优化算法的一种,广泛应用于约束优化问题。 考虑这样一种情况:我们得到了一种可微优化方法,可以优化特定的参数,但这些参数有一个”可行域“的约束条件,更新前后的参数都不能越过这个可行域。怎么办呢? 普通的梯度下降,每次计算损失函数后,需要反向传播计算梯度并更新参数。而投影梯度...
Projected Gradient Descent(投影梯度下降)是一种优化算法,用于解决约束优化问题。它的基本思想是在满足约束条件的可行解集合中,寻找使得目标函数最小化的解。 投影梯度下降的公式解析如下: 假设我们的目标函数为f(x),x是我们想要优化的变量,我们的约束条件是x必须满足C。我们的目标是在满足约束C的情况下,找到使f(...
We propose a projected semi-stochastic gradient descent method with mini-batch for improving both the theoretical complexity and practical performance of the general stochastic gradient descent method (SGD). We are able to prove linear convergence under weak strong convexity assumption. This requires no...
Projected gradient descent with momentum Here we augment the basic PGD algorithm of Eq. (5) with a technique borrowed from the momentum-aided gradient descent method from the field of machine learning.26 This technique stores a running weighted-average M k of the log-likelihood gradient. This ...
Projected gradient descent satifies:Theorem 3.4:f:dom(f)→R be convex and differentiable. Suppose f is smooth with parameter L. Choosing stepsize: γ=1L. Projected gradient descent satifies:f(xT)−f(x∗)≤L2T||x0−x∗||2(20)(20)f(xT)−f(x∗)≤L2T||x0−x∗||2...
Fast low-rank estimation by projected gradient descent:general statistical and algorithmic guarantees. Chen Y,Wainwright M J. . 2015Y. Chen and M. J. Wainwright, "Fast low-rank estimation by projected gradient descent: general statistical and algorithmic guarantees," CoRR, vol. abs/1509.03025, ...
The convergence results are also derived in the particular case in which the problem is unconstrained and even if inexact directions are taken as descent directions. Furthermore, we investigate the application of the proposed method to optimization models where the domain of the variable order map ...
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 analyzed. We first consider a bounded constraint set of the unknown parameter. Under some standard regularity assumptions, we provide an explicit...
What is a good step size for gradient descent? Why is the gradient the steepest ascent? Why is gradient steepest ascent? Why the Newton method is faster than gradient descent? Let r = <x, y, x>. Prove that gradient \ln ||r|| = \frac{r}{||r||^2} . Consider the following. f...