Asynchronous Distributed Composite Optimization via Publish-Subscribe Paradigm

Distributed optimization is essential for large-scale applications such as machine learning, power systems, and cooperative control. However, traditional methods are typically synchronous, which leads to resource underutilization and vulnerability to node failures. Although there has been considerable research on asynchronous algorithms, most existing work primarily focuses on synchronization decoupling, while temporal and spatial decoupling - both critical for practical distributed systems - remain largely unaddressed. This paper presents a robust asynchronous distributed composite optimization framework based on the publish-subscribe (pub/sub) paradigm. We first develop a distributed optimization algorithm that is robust to communication noise under a synchronous communication paradigm. By subsequently replacing the synchronous communication mechanism with an asynchronous publish-subscribe (pub/sub) architecture, the algorithm naturally inherits robustness to asynchrony, delays, and dynamic node participation. This approach achieves temporal, spatial, and synchronization decoupling, enabling resilient, highly scalable, and delay-tolerant distributed optimization. Experimental results on a multi-agent logistic regression task demonstrate the method's robustness to communication noise, delays, and dynamic node failures. The results show linear convergence rates in asynchronous settings, seamless adaptation to delayed node participation, and resilience to intermittent node outages.