Design and Analysis of Multi-Layer Decomposition for Resource Allocation

A distributed framework is proposed for addressing resource sharing problems in communications, micro-economics, and various other network systems. The approach uses a hierarchical multi-layer decomposition for network utility maximization. This methodology uses central management and distributed computations to allocate resources, and in dynamic environments, it aims to efficiently respond to network changes. The main contributions include a comprehensive description of an exemplary unifying optimization framework to share resources across different operators and platforms, and a detailed analysis of the generalized methods under the assumption that the network changes are on the same time-scale as the convergence time of the algorithms employed for local computations.Assuming strong concavity and smoothness of the objective functions, and under some stability conditions for each layer, convergence rates and optimality bounds are presented. The effectiveness of the framework is demonstrated through numerical examples. Furthermore, a novel Federated Edge Network Utility Maximization (FEdg-NUM) architecture is proposed for solving large-scale distributed network utility maximization problems in a fully decentralized way. In FEdg-NUM, clients with private utilities communicate with a peer-to-peer network of edge servers. Convergence properties are examined both through analysis and numerical simulations, and potential applications are highlighted. Finally, problems in a complex stochastic dynamic environment, specifically motivated by resource sharing during disasters occurring in multiple areas, are studied. In a hierarchical management scenario, a method of applying a primal-dual algorithm in higher-layer along with deep reinforcement learning algorithms in localities is presented. Analytical details as well as case studies such as pandemic and wildfire response are provided.