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

We develop two compression based stochastic gradient algorithms to solve aclass of non-smooth strongly convex-strongly concave saddle-point problems in adecentralized setting (without a central server). Our first algorithm is aRestart-based Decentralized Proximal Stochastic Gradient method withCompression (C-RDPSG) for general stochastic settings. We provide rigoroustheoretical guarantees of C-RDPSG with gradient computation complexity andcommunication complexity of order $\mathcal{O}( (1+\delta)^4\frac{1}{L^2}{\kappa_f^2}\kappa_g^2 \frac{1}{\epsilon} )$, to achieve an$\epsilon$-accurate saddle-point solution, where $\delta$ denotes thecompression factor, $\kappa_f$ and $\kappa_g$ denote respectively the conditionnumbers of objective function and communication graph, and $L$ denotes thesmoothness parameter of the smooth part of the objective function. Next, wepresent a Decentralized Proximal Stochastic Variance Reduced Gradient algorithmwith Compression (C-DPSVRG) for finite sum setting which exhibits gradientcomputation complexity and communication complexity of order $\mathcal{O}\left((1+\delta) \max \{\kappa_f^2, \sqrt{\delta}\kappa^2_f\kappa_g,\kappa_g \}\log\left(\frac{1}{\epsilon}\right) \right)$. Extensive numerical experimentsshow competitive performance of the proposed algorithms and provide support tothe theoretical results obtained.

Stochastic Gradient Methods with Compressed Communication for Decentralized Saddle Point Problems