  We propose iterative algorithms to solve adversarial problems in a variety of
supervised learning settings of interest. Our algorithms, which can be
interpreted as suitable ascent-descent dynamics in Wasserstein spaces, take the
form of a system of interacting particles. These interacting particle dynamics
are shown to converge toward appropriate mean-field limit equations in certain
large number of particles regimes. In turn, we prove that, under certain
regularity assumptions, these mean-field equations converge, in the large time
limit, toward approximate Nash equilibria of the original adversarial learning
problems. We present results for nonconvex-nonconcave settings, as well as for
nonconvex-concave ones. Numerical experiments illustrate our results.
