Distributed Methods for Large-Scale Optimization, Learning, and Games.

다국어 초록 (Multilingual Abstract)

The proliferation of large-scale networked multi-agent systems has necessitated the development of distributed methods especially when centralized solutions are impractical due to constraints on communication, computation, or privacy. This dissertation develops novel distributed methods for optimization, learning, and Nash equilibrium seeking in multi-agent systems, with a particular emphasis on addressing time-varying directed communication networks—one of the most challenging and largely unresolved problems in the field. Existing literature predominantly focuses on static, bidirectional or weight-balanced networks, as analyzing time-varying asymmetric information flows presents significant theoretical difficulties. However, time-varying directed communication networks are fundamental to many critical applications, including autonomous systems, sensor networks, and federated learning, where communication links frequently change due to mobility, bandwidth fluctuations, failures, or heterogeneous transmission capabilities.This dissertation provides a rigorous and comprehensive framework for handling time-varying directed information flows, introducing novel consensus-based algorithmic solutions and convergence analyses that overcome these long-standing theoretical and practical barriers. A key contribution is the development of two novel contraction properties that redefine convergence analysis and stability guarantees for distributed algorithms in time-varying directed networks. These contraction relations rigorously characterize the information exchange process governed by the pulling and pushing mechanisms through row-stochastic and column-stochastic weight matrices, providing explicit learning rate conditions and convergence bounds directly in terms of communication connectivity and problem-specific properties.