A scenario-based approach to multi-agent optimization with distributed information. Issue 2 (2020) - Falsone, Alessandro; Margellos, Kostas; Prandini, Maria; Garatti, Simone
Abstract: In this paper, we consider optimization problems involving multiple agents. Each agent introduces its own constraints on the optimization vector, and the constraints of all agents depend on a common source of uncertainty. We suppose that uncertainty is known locally to each agent through a private set of data (multi-agent scenarios), and that each agent enforces its scenario-based constraints to the solution of the multi-agent optimization problem. Our goal is to assess the feasibility properties of the corresponding multi-agent scenario solution. In particular, we are able to provide a priori certificates that the solution is feasible for a new occurrence of the global uncertainty with a probability that depends on the size of the datasets and the desired confidence level. The recently introduced wait-and-judge approach to scenario optimization and the notion of support rank are used for this purpose. Notably, decision-coupled and constraint-coupled uncertain optimization programs for multi-agent systems fit our framework and, hence, any distributed optimization scheme to solve the associated multi-agent scenario problem can be accompanied with our a priori probabilistic feasibility certificates.