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 study the convergence of Stochastic Gradient Descent (SGD) for stronglyconvex objective functions. We prove for all $t$ a lower bound on the expectedconvergence rate after the $t$-th SGD iteration; the lower bound is over allpossible sequences of diminishing step sizes. It implies that recently proposedsequences of step sizes at ICML 2018 and ICML 2019 are {\em universally} closeto optimal in that the expected convergence rate after {\em each} iteration iswithin a factor $32$ of our lower bound. This factor is independent ofdimension $d$. We offer a framework for comparing with lower bounds instate-of-the-art literature and when applied to SGD for strongly convexobjective functions our lower bound is a significant factor $775\cdot d$ largercompared to existing work.

Tight Dimension Independent Lower Bound on the Expected Convergence Rate for Diminishing Step Sizes in SGD