  We introduce a new approach for computing optimal equilibria via learning in
games. It applies to extensive-form settings with any number of players,
including mechanism design, information design, and solution concepts such as
correlated, communication, and certification equilibria. We observe that
optimal equilibria are minimax equilibrium strategies of a player in an
extensive-form zero-sum game. This reformulation allows to apply techniques for
learning in zero-sum games, yielding the first learning dynamics that converge
to optimal equilibria, not only in empirical averages, but also in iterates. We
demonstrate the practical scalability and flexibility of our approach by
attaining state-of-the-art performance in benchmark tabular games, and by
computing an optimal mechanism for a sequential auction design problem using
deep reinforcement learning.
