A Unified Framework for Robust Distributed Optimization Under Bounded Disturbances

Distributed optimization in networked systems has garnered significant attention in recent years, owing to its wideranging applications in fields such as multi-robot control, sensor networks, and large-scale machine learning. This paper introduces a novel unified framework for robust distributed optimization (RDO) under bounded disturbances. For this algorithmic framework, we derive its rate of convergence and prove its input-to-state stability when subject to unknown bounded disturbances. This new framework offers two key advantages. First, it generalizes existing RDO algorithms, enabling refinements that relax the conditions on step-size and accelerate convergence. Second, it provides valuable insights for the development of new RDO algorithms. To illustrate the effectiveness of our approach, we present experimental results on a distributed source localization problem.