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 consider the minimization of a sum of an expectation-valuedcoordinate-wise $L_i$-smooth nonconvex function and a nonsmooth block-separableconvex regularizer. We propose an asynchronous variance-reduced algorithm,where in each iteration, a single block is randomly chosen to update itsestimates by a proximal variable sample-size stochastic gradient scheme, whilethe remaining blocks are kept invariant. Notably, each block employs asteplength that is in accordance with its block-specific Lipschitz constantwhile block-specific batch-sizes are random variables updated at a rate thatgrows either at a geometric or polynomial rate with the (random) number oftimes that block is selected. We show that every limit point for almost everysample path is a stationary point and establish the ergodic non-asymptotic rate$\mathcal{O}(1/K) $. Iteration and oracle complexity to obtain an$\epsilon$-stationary point are shown to be $\mathcal{O}(1/\epsilon)$ and$\mathcal{O}(1/\epsilon^2)$, respectively. Furthermore, under a $ \mu$-proximal Polyak-{\L}ojasiewicz (PL) condition with the batch size increasingat a geometric rate, we prove that the suboptimality diminishes at a {\emgeometric} rate, the {\em optimal} deterministic rate while iteration andoracle complexity to obtain an $\epsilon$-optimal solution are proven to be$\mathcal{O}( (L_{\rm max}/\mu) \ln(1/\epsilon))$ and $\mathcal{O}\left((L_{\rmave}/\mu) (1/\epsilon)^{1+c} \right)$ with $c\geq 0$, respectively. In pursuitof less aggressive sampling rates, when the batch sizes increase at apolynomial rate of degree $v \geq 1$, suboptimality decays at a correspondingpolynomial rate while the iteration and oracle complexity to obtain an$\epsilon-$optimal solution are provably $\mathcal{O} ( v(1/\epsilon)^{1/v})$and $\mathcal{O} \left(e^v v^{2v+1}(1/\epsilon)^{1+1/v}\right)$, respectively.

Asynchronous Variance-reduced Block Schemes for Composite Nonconvex Stochastic Optimization: Block-specific Steplengths and Adapted Batch-sizes