An active learning method for solving competitive multi-agent decision-making and control problems

We propose a scheme based on active learning to reconstruct private strategies executed by a population of interacting agents and predict an exact outcome of the underlying multi-agent interaction process, here identified as a stationary action profile. We envision a scenario where an external observer, endowed with a learning procedure, can make queries and observe the agents' reactions through private action-reaction mappings, whose collective fixed point corresponds to a stationary profile. By iteratively collecting sensible data and updating parametric estimates of the action-reaction mappings, we establish sufficient conditions to assess the asymptotic properties of the proposed active learning methodology so that, if convergence happens, it can only be towards a stationary action profile. This fact yields two main consequences: i) learning locally-exact surrogates of the action-reaction mappings allows the external observer to succeed in its prediction task, and ii) working with assumptions so general that a stationary profile is not even guaranteed to exist, the established sufficient conditions hence act also as certificates for the existence of such a desirable profile. Extensive numerical simulations involving typical competitive multi-agent control and decision-making problems illustrate the practical effectiveness of the proposed learning-based approach. The authors are with the IMT School for Advanced Studies Lucca, Piazza San Francesco 19, 55100, Lucca, Italy ({filippo.fabiani,