Quantized Decentralized Stochastic Learning over Directed Graphs

TL;DR

This paper introduces a quantized decentralized stochastic learning algorithm for directed graphs that reduces communication load while maintaining convergence rates, demonstrating significant speed-up in numerical evaluations.

Contribution

It proposes a novel quantized algorithm based on push-sum for directed graphs, achieving the same convergence as exact methods with less communication.

Findings

Achieves the same convergence rates as exact-communication algorithms.

Demonstrates significant speed-up in numerical evaluations.

Effective for both convex and non-convex loss functions.

Abstract

We consider a decentralized stochastic learning problem where data points are distributed among computing nodes communicating over a directed graph. As the model size gets large, decentralized learning faces a major bottleneck that is the heavy communication load due to each node transmitting large messages (model updates) to its neighbors. To tackle this bottleneck, we propose the quantized decentralized stochastic learning algorithm over directed graphs that is based on the push-sum algorithm in decentralized consensus optimization. More importantly, we prove that our algorithm achieves the same convergence rates of the decentralized stochastic learning algorithm with exact-communication for both convex and non-convex losses. Numerical evaluations corroborate our main theoretical results and illustrate significant speed-up compared to the exact-communication methods.