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

In recent years, the success of deep learning has inspired many researchersto study the optimization of general smooth non-convex functions. However,recent works have established pessimistic worst-case complexities for thisclass functions, which is in stark contrast with their superior performance inreal-world applications (e.g. training deep neural networks). On the otherhand, it is found that many popular non-convex optimization problems enjoycertain structured properties which bear some similarities to convexity. Inthis paper, we study the class of \textit{quasar-convex functions} to close thegap between theory and practice. We study the convergence of first ordermethods in a variety of different settings and under different optimalitycriterions. We prove complexity upper bounds that are similar to standardresults established for convex functions and much better that state-of-the-artconvergence rates of non-convex functions. Overall, this paper suggests that\textit{quasar-convexity} allows efficient optimization procedures, and we arelooking forward to seeing more problems that demonstrate similar properties inpractice.

On The Convergence of First Order Methods for Quasar-Convex Optimization