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We propose a scheme based on active learning to reconstruct privatestrategies executed by a population of interacting agents and predict an exactoutcome of the underlying multi-agent interaction process, here identified as astationary 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 fixedpoint corresponds to a stationary profile. By iteratively collecting sensibledata and updating parametric estimates of the action-reaction mappings, weestablish sufficient conditions to assess the asymptotic properties of theproposed active learning methodology so that, if convergence happens, it canonly be towards a stationary action profile. This fact yields two mainconsequences: i) learning locally-exact surrogates of the action-reactionmappings allows the external observer to succeed in its prediction task, andii) working with assumptions so general that a stationary profile is not evenguaranteed to exist, the established sufficient conditions hence act also ascertificates for the existence of such a desirable profile. Extensive numericalsimulations involving typical competitive multi-agent control anddecision-making problems illustrate the practical effectiveness of the proposedlearning-based approach.

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