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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We study the mean estimation problem under communication and localdifferential privacy constraints. While previous work has proposed\emph{order}-optimal algorithms for the same problem (i.e., asymptoticallyoptimal as we spend more bits), \emph{exact} optimality (in the non-asymptoticsetting) still has not been achieved. In this work, we take a step towardscharacterizing the \emph{exact}-optimal approach in the presence of sharedrandomness (a random variable shared between the server and the user) andidentify several conditions for \emph{exact} optimality. We prove that one ofthe conditions is to utilize a rotationally symmetric shared random codebook.Based on this, we propose a randomization mechanism where the codebook is arandomly rotated simplex -- satisfying the properties of the\emph{exact}-optimal codebook. The proposed mechanism is based on a $k$-closestencoding which we prove to be \emph{exact}-optimal for the randomly rotatedsimplex codebook.

Exact Optimality of Communication-Privacy-Utility Tradeoffs in Distributed Mean Estimation