A scenario-based approach to multi-agent optimization with distributed information⁎Research was partially supported by EPSRC UK, grant EP/P03277X/1. Issue 2 (2020)

• Record Type: Journal Article
• Authors: Falsone, Alessandro; Margellos, Kostas; Prandini, Maria; Garatti, Simone
• Is Part Of: IFAC-PapersOnLine. Volume 53:Issue 2(2020)
• Page Start: 20
• Page End: 25
• Publication Date: 2020
• Subjects: Uncertain systems -- multi-agent systems -- data-driven optimization -- distributed algorithms; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2020.12.034
• Languages: English
• ISSNs: 2405-8963

Abstract

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.