Dynamics based Privacy Preservation in Decentralized Optimization

TL;DR

This paper introduces a novel decentralized optimization algorithm that inherently preserves privacy by adding randomness to optimization parameters, maintaining accuracy and convergence without heavy computational overhead.

Contribution

It proposes a new privacy-preserving decentralized optimization method that leverages robustness to uncertainties, avoiding traditional privacy mechanisms like differential privacy or encryption.

Findings

The algorithm achieves R-linear convergence under smooth, strongly convex objectives.

Privacy is maintained without sacrificing optimization accuracy.

Numerical results confirm theoretical privacy and convergence guarantees.

Abstract

With decentralized optimization having increased applications in various domains ranging from machine learning, control, sensor networks, to robotics, its privacy is also receiving increased attention. Existing privacy-preserving approaches for decentralized optimization achieve privacy preservation by patching decentralized optimization with information-technology privacy mechanisms such as differential privacy or homomorphic encryption, which either sacrifices optimization accuracy or incurs heavy computation/communication overhead. We propose an inherently privacy-preserving decentralized optimization algorithm by exploiting the robustness of decentralized optimization to uncertainties in optimization dynamics. More specifically, we present a general decentralized optimization framework, based on which we show that privacy can be enabled in decentralized optimization by adding randomness in optimization parameters. We further show that the added randomness has no influence on the accuracy of optimization, and prove that our inherently privacy-preserving algorithm has $R$-linear convergence when the global objective function is smooth and strongly convex. We also rigorously prove that the proposed algorithm can avoid the gradient of a node from being inferable by other nodes. Numerical simulation results confirm the theoretical predictions.