Abstract

Motivated by the growing complexity of large-scale, heterogeneous optimization and control systems, this talk presents compositional and sheaf-theoretic semantics for distributed optimization and control. Compositional semantics, where the meaning of a whole is determined from the meanings of its parts, has been foundational to programming languages. This work shows that distributed optimization admits the same principled treatment. We construct a categorical and logical framework in which optimization problems, algorithms, and interconnection architectures are first-class compositional objects. Within this framework, optimization methods are realized as algebra morphisms from static objective specifications to dynamic semantics given by transition systems. This perspective yields compositional invariance theorems for a broad class of problem types and algorithmic techniques. On the applied side, we demonstrate that network sheaves provide a compositional data structure for organizing distributed optimization over graphs. The theory yields modular invariance results for systems assembled from heterogeneous subsystems, with applications spanning operations research, federated multi-task learning, and networked control. In particular, we leverage the sheaf Laplacian to derive a unified framework for asynchronous, heterogeneous multi-agent coordination and target tracking. Together, these results establish distributed optimization as a domain with rigorous compositional semantics, enabling modular design, analysis, and principled integration of optimization, control, and networked computation.

About the Speaker

Tyler Hanks is a graduate research assistant in the GATAS (General Algebraic Techniques Advancing Science) lab in the Computer and Information Science and Engineering Department at the University of Florida. He obtained his Ph.D. and M.S. in Computer Science from the University of Florida and his B.S. in Computer Science from the University of South Florida, graduating magna cum laude with a minor in astronomy. His research develops categorical and sheaf-theoretic frameworks for modular specification and analysis of multi-agent systems, with applications to federated learning, networked control, and distributed optimization in heterogeneous settings. Hanks completed three summer internships at the Information Directorate of the Air Force Research Lab and plans to continue research into compositional and formal methods for intelligent multi-agent systems. He is a recipient of the NSF Graduate Research Fellowship, has published in IEEE control theory venues, and has presented at numerous international conferences.