Robust Distributed Nonconvex Optimization Enabling Communication Acceleration and Privacy Protection

TL;DR

This paper introduces a robust distributed nonconvex optimization algorithm that enhances privacy and communication efficiency by using noise obfuscation and acceleration techniques, with proven convergence and empirical validation.

Contribution

The paper proposes RPP, a novel privacy-preserving distributed optimization algorithm with noise robustness and accelerated convergence, achieving optimal communication complexity.

Findings

RPP converges to a stationary point at a sublinear rate.

The accelerated RPP achieves optimal communication complexity.

Numerical experiments confirm robustness and efficiency of the proposed methods.

Abstract

This paper addresses a distributed nonconvex optimization problem over multi-agent networks, where each agent exchanges its local information solely with its neighbors. Given that most existing distributed nonconvex optimization algorithms are susceptible to information leakage during inter agent communications, we propose a Robust Proximal Primal dual algorithm, referred to as RPP, to enhance the security of information transmission. In contrast to many existing approaches that directly transmit local variables throughout the network, we introduce carefully designed random noises to obfuscate sensitive local information. This not only preserves privacy but also demonstrates the noise robustness of our proposed algorithm. We establish a sublinear rate at which RPP converges to a stationary solution. Moreover, by incorporating Chebyshev acceleration, an accelerated variant of RPP is developed and achieves the optimal communication complexity bound for the algorithms that allow for exchanging local deci sions at each iteration. The superior convergence performance of RPP is validated through a few numerical experiments, which also indicate that, within an appropriate range, the introduced perturbations do not impede the convergence speed of RPP.