Distributed optimization methods for N-cluster games

Abstract

Abstract This work provides methodological approaches to solve convex optimization problems arising in multi-agent systems which can be reformulated in terms of a so called N-cluster game. We consider different settings of information available to each agent in the system. First, we present a centralized algorithm, which requires a central coordinator having full access to information about agents’ actions and gradients of their cost functions, to demonstrate how the standard gradient descent method can be applied to achieve an optimal output in N-cluster games. After that we relax the full information setting and assume that only partial information is available to each agent. Focus lies on the following two cases. In the first case, the agents have access to their gradient functions and are allowed to exchange information with their local neighbors over a communication graph that connects the whole system. In the second case, the agents do not know the functional form of their objectives/gradients and can only access the current values of their objective functions at some query point. Moreover, the agents are allowed to communicate only with their local neighbors within the cluster to which they belong. For both settings we present the convergent optimization procedures and analyse their efficiency in simulations.