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Caltech

CMX Lunch Seminar

Wednesday, May 29, 2024
12:00pm to 1:00pm
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Annenberg 213
Adversarial training and the generalized Wasserstein barycenter problem
Matthew Jacobs, Assistant Professor, Department of Mathematics, University of California Santa Barbara,

Adversarial training is a framework widely used by practitioners to enforce robustness of machine learning models. During the training process, the learner is pitted against an adversary who has the power to alter the input data. As a result, the learner is forced to build a model that is robust to data perturbations. Despite the importance and relative conceptual simplicity of adversarial training, there are many aspects that are still not well-understood (e.g. regularization effects, geometric/analytic interpretations, tradeoff between accuracy and robustness, etc...), particularly in the case of multiclass classification.

In this talk, I will show that in the non-parametric setting, the adversarial training problem is equivalent to a multimarginal optimal transport problem that can be viewed as a generalized version of the Wasserstein barycenter problem. The connection between these problems allows us to completely characterize the optimal adversarial strategy and to bring in tools from optimal transport to analyze and compute optimal classifiers. This also has implications for the parametric setting, as the value of the generalized barycenter problem gives a universal upper bound on the robustness/accuracy tradeoff inherent to adversarial training.

For more information, please contact Jolene Brink by phone at (626)395-2813 or by email at [email protected] or visit CMX Website.