Convergence and Privacy of Decentralized Nonconvex Optimization with Gradient Clipping and Communication Compression

TL;DR

This paper introduces PORTER, a novel framework analyzing how gradient clipping and communication compression affect convergence and privacy in decentralized nonconvex optimization, providing the first such analysis without bounded gradient assumptions.

Contribution

It presents the first convergence analysis for decentralized nonconvex optimization with gradient clipping and communication compression, including privacy considerations.

Findings

PORTER-DP enables local differential privacy with Gaussian noise.

PORTER-GC stabilizes training in decentralized settings.

The analysis reveals trade-offs between convergence, compression, connectivity, and privacy.

Abstract

Achieving communication efficiency in decentralized machine learning has been attracting significant attention, with communication compression recognized as an effective technique in algorithm design. This paper takes a first step to understand the role of gradient clipping, a popular strategy in practice, in decentralized nonconvex optimization with communication compression. We propose PORTER, which considers two variants of gradient clipping added before or after taking a mini-batch of stochastic gradients, where the former variant PORTER-DP allows local differential privacy analysis with additional Gaussian perturbation, and the latter variant PORTER-GC helps to stabilize training. We develop a novel analysis framework that establishes their convergence guarantees without assuming the stringent bounded gradient assumption. To the best of our knowledge, our work provides the first convergence analysis for decentralized nonconvex optimization with gradient clipping and communication compression, highlighting the trade-offs between convergence rate, compression ratio, network connectivity, and privacy.