Distributed Optimization with Efficient Communication, Event-Triggered Solution Enhancement, and Operation Stopping
Apostolos I. Rikos, Wei Jiang, Themistoklis Charalambous, Karl H. Johansson
TL;DR
The paper tackles distributed optimization over directed, bandwidth-constrained networks by introducing three algorithms that quantify communication, enable event-driven refinement, and support distributed termination. Algorithm 1 achieves linear convergence to a $\mathcal{O}(\u0004elta)$ neighborhood using quantized averaging; Algorithm 2 adds an event-triggered zooming mechanism to refine precision and decide when to stop; Algorithm 4 further extends to $N$-bit quantizers with a fixed-bit communication budget while still enabling distributed stopping. Across all methods, the convergence rate remains linear with a contraction factor of $1-\frac{\alpha \mu}{n}$ and the ultimate accuracy is governed by the quantization level or its adaptive variants, with finite-time consensus and zooming ensuring progress toward the optimum. An application to distributed sensor fusion for target localization demonstrates favorable convergence and reduced communication relative to existing literature. These results advance practical distributed optimization in directed, unbalanced networks by coupling efficient quantized communication with rigorous stopping criteria and refinement mechanisms.
Abstract
In modern large-scale systems with sensor networks and IoT devices it is essential to collaboratively solve complex problems while utilizing network resources efficiently. In our paper we present three distributed optimization algorithms that exhibit efficient communication among nodes. Our first algorithm presents a simple quantized averaged gradient procedure for distributed optimization, which is shown to converge to a neighborhood of the optimal solution. Our second algorithm incorporates a novel event-triggered refinement mechanism, which refines the utilized quantization level to enhance the precision of the estimated optimal solution. It enables nodes to terminate their operation according to predefined performance guarantees. Our third algorithm is tailored to operate in environments where each message consists of only a few bits. It incorporates a novel event-triggered mechanism for adjusting the quantizer basis and quantization level, allowing nodes to collaboratively decide operation termination based on predefined performance criteria. We analyze the three algorithms and establish their linear convergence. Finally, an application on distributed sensor fusion for target localization is used to demonstrate their favorable performance compared to existing algorithms in the literature.