Quantization enabled Privacy Protection in Decentralized Stochastic Optimization

TL;DR

This paper introduces a decentralized stochastic optimization algorithm that uses aggressive quantization, including ternary schemes, to ensure privacy through differential privacy guarantees without sacrificing convergence accuracy.

Contribution

It presents the first method combining quantization-based privacy with provable convergence in decentralized stochastic optimization for both convex and non-convex functions.

Findings

Achieves differential privacy through quantization without losing convergence accuracy.

Supports aggressive quantization schemes like ternary quantization.

Validated effectiveness through simulations and experiments.

Abstract

By enabling multiple agents to cooperatively solve a global optimization problem in the absence of a central coordinator, decentralized stochastic optimization is gaining increasing attention in areas as diverse as machine learning, control, and sensor networks. Since the associated data usually contain sensitive information, such as user locations and personal identities, privacy protection has emerged as a crucial need in the implementation of decentralized stochastic optimization. In this paper, we propose a decentralized stochastic optimization algorithm that is able to guarantee provable convergence accuracy even in the presence of aggressive quantization errors that are proportional to the amplitude of quantization inputs. The result applies to both convex and non-convex objective functions, and enables us to exploit aggressive quantization schemes to obfuscate shared information, and hence enables privacy protection without losing provable optimization accuracy. In fact, by using a {stochastic} ternary quantization scheme, which quantizes any value to three numerical levels, we achieve quantization-based rigorous differential privacy in decentralized stochastic optimization, which has not been reported before. In combination with the presented quantization scheme, the proposed algorithm ensures, for the first time, rigorous differential privacy in decentralized stochastic optimization without losing provable convergence accuracy. Simulation results for a distributed estimation problem as well as numerical experiments for decentralized learning on a benchmark machine learning dataset confirm the effectiveness of the proposed approach.