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

Variance reduction techniques such as SPIDER/SARAH/STORM have beenextensively studied to improve the convergence rates of stochastic non-convexoptimization, which usually maintain and update a sequence of estimators for asingle function across iterations. What if we need to track multiple functionalmappings across iterations but only with access to stochastic samples of$\mathcal{O}(1)$ functional mappings at each iteration? There is an importantapplication in solving an emerging family of coupled compositional optimizationproblems in the form of $\sum_{i=1}^m f_i(g_i(\mathbf{w}))$, where $g_i$ isaccessible through a stochastic oracle. The key issue is to track and estimatea sequence of $\mathbf g(\mathbf{w})=(g_1(\mathbf{w}), \ldots,g_m(\mathbf{w}))$ across iterations, where $\mathbf g(\mathbf{w})$ has $m$blocks and it is only allowed to probe $\mathcal{O}(1)$ blocks to attain theirstochastic values and Jacobians. To improve the complexity for solving theseproblems, we propose a novel stochastic method named Multi-block-Single-probeVariance Reduced (MSVR) estimator to track the sequence of $\mathbfg(\mathbf{w})$. It is inspired by STORM but introduces a customized errorcorrection term to alleviate the noise not only in stochastic samples for theselected blocks but also in those blocks that are not sampled. With the help ofthe MSVR estimator, we develop several algorithms for solving theaforementioned compositional problems with improved complexities across aspectrum of settings with non-convex/convex/stronglyconvex/Polyak-{\L}ojasiewicz (PL) objectives. Our results improve upon priorones in several aspects, including the order of sample complexities anddependence on the strong convexity parameter. Empirical studies on multi-taskdeep AUC maximization demonstrate the better performance of using the newestimator.

Multi-block-Single-probe Variance Reduced Estimator for Coupled Compositional Optimization