On adversarial robustness and the use of Wasserstein ascent-descent dynamics to enforce it

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 d...

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Bibliographic Details
Published in:arXiv.org 2023-01
Main Authors: Camilo Garcia Trillos, Nicolas Garcia Trillos
Format: Article
Language:English
Subjects:
Ascent
Convergence
Iterative algorithms
Iterative methods
Machine learning
Mathematical analysis
Robustness (mathematics)
Supervised learning
Online Access:Get full text
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Summary: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.
ISSN:2331-8422