In this article, we delve into the realm of distributed optimization and explore a novel approach called Multi-Gossip Skip (MG-SKIP). By leveraging gossip communication and probabilistic local updates, MG-SKIP offers a promising solution to enhance the dependence on network topology while accelerating the communication complexity. We conduct two numerical experiments to validate the theoretical results and provide insights into the performance of MG-SKIP.
Theory
Motivated by the seminal work in [10], we propose MG-SKIP, a distributed optimization algorithm that incorporates random communication skipping. By partitioning the updates among nodes based on their connectivity patterns, MG-SKIP reduces the number of communication hops required for convergence. Moreover, by adding extra averaging steps through multi-round gossip communication, we accelerate the average consensus process.
Comparison
To ascertain the effectiveness of MG-SKIP, we perform a comparative analysis with existing deterministic distributed optimization algorithms. Our results reveal that MG-SKIP exhibits improved convergence rates and reduced communication complexity compared to existing methods. Furthermore, MG-SKIP demonstrates enhanced topology dependence, which can be particularly beneficial in dynamic networks.
Experiments
We conduct two numerical experiments to validate the theoretical findings and assess the performance of MG-SKIP. The first experiment focuses on synthetic datasets with varying stepsize conditions, while the second experiment investigates the impact of communication skipping on real-world networks. Our results demonstrate that MG-SKIP consistently outperforms existing methods in terms of convergence rate and communication complexity.
Conclusion
In conclusion, this article introduces Multi-Gossip Skip (MG-SKIP), a novel distributed optimization algorithm that combines gossip communication with probabilistic local updates to enhance the dependence on network topology while accelerating the communication complexity. Through comprehensive numerical experiments, we demonstrate the effectiveness of MG-SKIP and highlight its potential applications in dynamic networks. By providing a comparative study and in-depth analysis, this work contributes significantly to the field of distributed optimization and gossip protocols.
