Exact Optimality of Communication-Privacy-Utility Tradeoffs in Distributed Mean Estimation
- Authors
- Isik, Berivan; Chen, Wei-Ning; Ozgur, Ayfer; Weissman, Tsachy; No, Albert
- Issue Date
- 2023
- Publisher
- Neural information processing systems foundation
- Citation
- Advances in Neural Information Processing Systems, v.36
- Journal Title
- Advances in Neural Information Processing Systems
- Volume
- 36
- URI
- https://scholarworks.bwise.kr/hongik/handle/2020.sw.hongik/33202
- ISSN
- 1049-5258
- Abstract
- We study the mean estimation problem under communication and local differential privacy constraints. While previous work has proposed order-optimal algorithms for the same problem (i.e., asymptotically optimal as we spend more bits), exact optimality (in the non-asymptotic setting) still has not been achieved. In this work, we take a step towards characterizing the exact-optimal approach in the presence of shared randomness (a random variable shared between the server and the user) and identify several conditions for exact optimality. We prove that one of the 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 properties of the exact-optimal codebook. The proposed mechanism is based on a k-closest encoding which we prove to be exact-optimal for the randomly rotated simplex codebook. © 2023 Neural information processing systems foundation. All rights reserved.
- Files in This Item
- There are no files associated with this item.
- Appears in
Collections - College of Engineering > School of Electronic & Electrical Engineering > 1. Journal Articles
![qrcode](https://api.qrserver.com/v1/create-qr-code/?size=55x55&data=https://scholarworks.bwise.kr/hongik/handle/2020.sw.hongik/33202)
Items in ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.