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

In this work, we conduct the first systematic study of stochastic variationalinequality (SVI) and stochastic saddle point (SSP) problems under theconstraint of differential privacy (DP). We propose two algorithms: NoisyStochastic Extragradient (NSEG) and Noisy Inexact Stochastic Proximal Point(NISPP). We show that a stochastic approximation variant of these algorithmsattains risk bounds vanishing as a function of the dataset size, with respectto the strong gap function; and a sampling with replacement variant achievesoptimal risk bounds with respect to a weak gap function. We also show lowerbounds of the same order on weak gap function. Hence, our algorithms areoptimal. Key to our analysis is the investigation of algorithmic stabilitybounds, both of which are new even in the nonprivate case. The dependence ofthe running time of the sampling with replacement algorithms, with respect tothe dataset size $n$, is $n^2$ for NSEG and $\tilde{O}(n^{3/2})$ for NISPP.

Optimal Algorithms for Differentially Private Stochastic Monotone Variational Inequalities and Saddle-Point Problems