Robust SVM Optimization in Banach spaces
This work addresses robust classification for machine learning in infinite-dimensional spaces, but it appears incremental as it extends existing SVM theory to Banach spaces.
The authors tackled binary classification in Banach spaces with uncertainty by generalizing classical SVM results, including the Representer Theorem and strong duality, to robust counterparts, and proposed a game-theoretic interpretation for finding closest points in convex sets in reflexive, smooth spaces.
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.