Robust SVM Optimization in Banach spaces

• URL: http://arxiv.org/abs/2202.08567v1
• Date: Thu, 17 Feb 2022 10:32:06 GMT
• Title: Robust SVM Optimization in Banach spaces
• Authors: Mohammed Sbihi and Nicolas Couellan
• Abstract summary: We show that a number of results from classical support vector machines theory can be appropriately generalised to their robust counterpart in Banach spaces. These include the Representer Theorem, strong duality for the associated Optimization problem as well as their geometric interpretation.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We address the issue of binary classification in Banach spaces in presence of uncertainty. We show that a number of results from classical support vector machines theory can be appropriately generalised to their robust counterpart in Banach spaces. These include the Representer Theorem, strong duality for the associated Optimization problem as well as their geometric interpretation. Furthermore, we propose a game theoretic interpretation by expressing a Nash equilibrium problem formulation for the more general problem of finding the closest points in two closed convex sets when the underlying space is reflexive and smooth.

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