The END: Estimation Network Design for Games under Partial-decision Information

Multi-agent decision problems are typically solved via distributed iterative algorithms, where the agents only communicate between themselves on a peerto- peer network. Each agent usually maintains a copy of each decision variable, while agreement among the local copies is enforced via consensus protocols. Yet, each agent is often directly influenced by a small portion of the decision variables only: neglecting this sparsity results in redundancy, poor scalability with the network size, communication and memory overhead. To address these challenges, we develop Estimation Network Design (END), a framework for the design and analysis of distributed algorithms. END algorithms can be tuned to exploit problem-specific sparsity structures, by optimally allocating copies of each variable only to a subset of agents, to improve efficiency and minimize redundancy. We illustrate the END's potential on generalized Nash equilibrium (GNE) seeking under partial-decision information, by designing new algorithms that can leverage the sparsity in cost functions, constraints and aggregation values, and by relaxing the assumptions on the (directed) communication network postulated in the literature. Finally, we test numerically our methods on a unicast rate allocation problem, revealing greatly reduced communication and memory costs.