Decentralized Optimization via RC-ALADIN with Efficient Quantized Communication

TL;DR

This paper proposes a decentralized optimization algorithm that combines RC-ALADIN with quantized communication, achieving linear convergence to a neighborhood of the optimal solution under strong convexity and smoothness assumptions, while reducing communication costs.

Contribution

It introduces a novel decentralized optimization method integrating RC-ALADIN with quantized communication, ensuring convergence with limited bandwidth.

Findings

Achieves linear convergence to a neighborhood of the optimum.

Performs favorably compared to existing algorithms in experiments.

Reduces communication overhead through quantization.

Abstract

In this paper, we investigate the problem of decentralized consensus optimization over directed graphs with limited communication bandwidth. We introduce a novel decentralized optimization algorithm that combines the Reduced Consensus Augmented Lagrangian Alternating Direction Inexact Newton (RC-ALADIN) method with a finite time quantized coordination protocol, enabling quantized information exchange among nodes. Assuming the nodes' local objective functions are $\mu$-strongly convex and simply smooth, we establish global convergence at a linear rate to a neighborhood of the optimal solution, with the neighborhood size determined by the quantization level. Additionally, we show that the same convergence result also holds for the case where the local objective functions are convex and $L$-smooth. Numerical experiments demonstrate that our proposed algorithm compares favorably against algorithms in the current literature while exhibiting communication efficient operation.