… The problem we address in this article is: Do ADAGRAD algorithms provably avoid saddle
points? This saddle avoidance type question stimulates the study of non-convex optimization, …

… avoids convergence to undesired saddles–albeit not guarantees convergence on a general
non-convex-concave saddle point … We compare Cesp to the vanilla Adagrad optimizer. …

… the real anisotropic curvature; (3) Technically, it is difficult to avoid explicit existence of d
in the final convergence bound of AdaGrad if Eqn. (10) is employed, for instance, even the …

… In this paper, we present a simplified and unified proof of convergence to a critical point
for Adagrad and Adam for stochastic non-convex smooth optimization. We assume that the …

… Methods with adaptive scaling of different features play a key role in solving saddle point …
is it avoided. At the moment this assumption can be found in the literature on saddle point …

… of escaping the saddle points and avoiding overfitting, while … of the simple average
one in AdaGrad. In particular, Adam is … proof of the existence of critical points under non-convexity …

… To experimentally show that the cross-dependency term can either improve or worsen the
convergence rate of Adagrad, we design specific problems based on the knowledge about the …

… However, as a fundamental adaptive optimizer, the theoretical analysis of AdaGrad-Norm is
… AdaGrad-Norm. We propose novel techniques that avoid the assumption of no saddle points …

… escape from saddle points by adaptive methods [41… SGD, AMSGrad-norm, and AdaGrad-norm
– to establish a universal observation that they avoid exponential dependency in ℓ without …

… to alleviate the limitations of AdaGrad. RMSprop scales the gradient … Yogi, has similar updates
as AdaGrad but allows for the … First-order methods almost always avoid saddle points: The …