English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The alternating gradient descent (AGD) is a simple but popular algorithmwhich has been applied to problems in optimization, machine learning, dataming, and signal processing, etc. The algorithm updates two blocks of variablesin an alternating manner, in which a gradient step is taken on one block, whilekeeping the remaining block fixed. When the objective function is nonconvex, itis well-known the AGD converges to the first-order stationary solution with aglobal sublinear rate.  In this paper, we show that a variant of AGD-type algorithms will not betrapped by "bad" stationary solutions such as saddle points and local maximumpoints. In particular, we consider a smooth unconstrained optimization problem,and propose a perturbed AGD (PA-GD) which converges (with high probability) tothe set of second-order stationary solutions (SS2) with a global sublinearrate. To the best of our knowledge, this is the first alternating typealgorithm which takes $\mathcal{O}(\text{polylog}(d)/\epsilon^{7/3})$iterations to achieve SS2 with high probability [where polylog$(d)$ ispolynomial of the logarithm of dimension $d$ of the problem].

On the Sublinear Convergence of Randomly Perturbed Alternating Gradient Descent to Second Order Stationary Solutions