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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Consider a distributed non-convex optimization problem, in which a number of agents connected by a network G collectively optimize a sum of smooth and non-convex local objective functions. We address the following important question: For a class of unconstrained problems, if only local gradient information is available, what is the fastest rate that distributed algorithms can achieve, and how to achieve those rates. We perform a lower bound analysis for a class of first-order distributed methods which only utilizes local gradient information. We show that in the worst-case it takes at least O(1/&#x221A;(&#x03BE;(G))&#x00D7;L/&#x03B5;) iterations to achieve certain &#x03B5;-solution, where &#x03BE;(G) represents the spectrum gap of the graph Laplacian matrix, and L is some Lipschitz constant. Further, for a general problem class, we propose rate-optimal methods whose rates match the lower bounds (up to a polylog factor). To the best of our knowledge, this is the first time that lower rate bounds and optimal methods have been developed for distributed non-convex optimization problems.

Distributed Non-Convex First-Order optimization and Information Processing: Lower Complexity Bounds and Rate Optimal Algorithms