Breaking the Communication-Privacy-Accuracy Trilemma

TL;DR

This paper introduces novel encoding and decoding methods that simultaneously optimize privacy and communication efficiency in distributed learning tasks, achieving near-optimal accuracy under local differential privacy and communication constraints.

Contribution

It develops new mechanisms for mean, frequency, and distribution estimation that are optimal across various privacy and communication settings, filling a gap in existing research.

Findings

Achieves order-optimal mean estimation error under privacy and communication constraints.

Develops a frequency estimation mechanism with optimal error for all privacy levels and budgets.

Constructs a distribution estimation method that is rate-optimal across regimes.

Abstract

Two major challenges in distributed learning and estimation are 1) preserving the privacy of the local samples; and 2) communicating them efficiently to a central server, while achieving high accuracy for the end-to-end task. While there has been significant interest in addressing each of these challenges separately in the recent literature, treatments that simultaneously address both challenges are still largely missing. In this paper, we develop novel encoding and decoding mechanisms that simultaneously achieve optimal privacy and communication efficiency in various canonical settings. In particular, we consider the problems of mean estimation and frequency estimation under $\varepsilon$-local differential privacy and $b$-bit communication constraints. For mean estimation, we propose a scheme based on Kashin's representation and random sampling, with order-optimal estimation error under both constraints. For frequency estimation, we present a mechanism that leverages the recursive structure of Walsh-Hadamard matrices and achieves order-optimal estimation error for all privacy levels and communication budgets. As a by-product, we also construct a distribution estimation mechanism that is rate-optimal for all privacy regimes and communication constraints, extending recent work that is limited to $b=1$ and $\varepsilon=O(1)$. Our results demonstrate that intelligent encoding under joint privacy and communication constraints can yield a performance that matches the optimal accuracy achievable under either constraint alone.