The END: Estimation Network Design for efficient distributed equilibrium seeking

Multi-agent decision problems are typically solved via distributed algorithms, where the computational burden is partitioned among a group of agents, only allowed to communicate on a peer-to-peer network. To cope with the limited information available, each processor is required to store a copy of certain variables, while agreement among the local copies is enforced via consensus protocols. This structure often leads to redundancy of the information, poor scalability with the network size, communication and memory overhead. In this paper, we develop a framework for the design and analysis of distributed algorithms, named END, to systematically assign local copies only to a subset of the agents, while still ensuring consistency. END unifies and generalizes several existing (application-specific) approaches, and leverages the original sparsity of the problem to improve efficiency and minimize redundancy. We illustrate the flexibility and potential of END for several methods in the context of consensus optimization and game equilibrium seeking.