The field of distributed optimization and 6G networks is rapidly advancing, with a focus on developing innovative methods for efficient and reliable communication. Recent developments have highlighted the importance of asynchronous and decentralized approaches, which can effectively handle heterogeneous computation speeds and unpredictable communication delays. Notably, the integration of artificial intelligence (AI) and space-air-ground integrated networks (SAGIN) is becoming increasingly significant, with AI playing a pivotal role in managing complex control and enhancing automation and flexibility. Furthermore, the concept of reliability coverage has emerged as a key factor in designing local 6G networks that meet reliability and latency targets.

Noteworthy papers in this area include:

• Streaming Krylov-Accelerated Stochastic Gradient Descent, which presents a novel optimization approach that accelerates convergence for ill-conditioned problems.
• Argus: Federated Non-convex Bilevel Learning over 6G Space-Air-Ground Integrated Network, which develops a novel asynchronous algorithm for tackling non-convex and non-smooth decentralized federated bilevel learning over SAGIN.
• Birch SGD: A Tree Graph Framework for Local and Asynchronous SGD Methods, which proposes a new unifying framework for analyzing and designing distributed SGD methods.
• Asynchronous Decentralized SGD under Non-Convexity: A Block-Coordinate Descent Framework, which introduces a refined model of Asynchronous Decentralized Stochastic Gradient Descent under practical assumptions of bounded computation and communication times.