García Trillos, Camilo Andrés; García Trillos, Nicolás; (2024) On adversarial robustness and the use of Wasserstein ascent-descent dynamics to enforce it. Information and Inference: A Journal of the IMA , 13 (3) , Article iaae018. 10.1093/imaiai/iaae018.

Text ParticlesAdversarial-review.pdf - Accepted Version Access restricted to UCL open access staff until 6 August 2025. Download (759kB)

Abstract

We propose iterative algorithms to solve adversarial training 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 non-convex non-concave settings, as well as for non-convex concave ones. Numerical experiments illustrate our results.

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