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- W4380136299 abstract "We study the mean estimation problem under communication and local differential privacy constraints. While previous work has proposed emph{order}-optimal algorithms for the same problem (i.e., asymptotically optimal as we spend more bits), emph{exact} optimality (in the non-asymptotic setting) still has not been achieved. In this work, we take a step towards characterizing the emph{exact}-optimal approach in the presence of shared randomness (a random variable shared between the server and the user) and identify several necessary conditions for emph{exact} optimality. We prove that one of the necessary conditions is to utilize a rotationally symmetric shared random codebook. Based on this, we propose a randomization mechanism where the codebook is a randomly rotated simplex -- satisfying the necessary properties of the emph{exact}-optimal codebook. The proposed mechanism is based on a $k$-closest encoding which we prove to be emph{exact}-optimal for the randomly rotated simplex codebook." @default.
- W4380136299 created "2023-06-10" @default.
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- W4380136299 date "2023-06-08" @default.
- W4380136299 modified "2023-09-27" @default.
- W4380136299 title "Exact Optimality of Communication-Privacy-Utility Tradeoffs in Distributed Mean Estimation" @default.
- W4380136299 doi "https://doi.org/10.48550/arxiv.2306.04924" @default.
- W4380136299 hasPublicationYear "2023" @default.
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