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- Title
On adversarial robustness and the use of Wasserstein ascent-descent dynamics to enforce it.
- Authors
Trillos, Camilo Andrés García; Trillos, Nicolás García
- 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.
- Subjects
SUPERVISED learning; NASH equilibrium; PARTICLE dynamics; LEARNING problems; ALGORITHMS
- Publication
Information & Inference: A Journal of the IMA, 2024, Vol 13, Issue 3, p1
- ISSN
2049-8764
- Publication type
Article
- DOI
10.1093/imaiai/iaae018