A learning-based approach to multi-agent decision-making

We propose a learning-based methodology to reconstruct private information held by a population of interacting agents in order to 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, is allowed to make queries and observe the agents’ reactions through private action-reaction mappings, whose collective ﬁxed point corresponds to a stationary proﬁle. By adopting a smart query process to iteratively collect sensible data and update parametric estimates, we establish suﬃcient conditions to assess the asymptotic properties of the proposed learning-based 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.