Theoretical aspects of robust SVM optimization in Banach spaces and Nash equilibrium interpretation

There are many real life applications where data can not be effectively represented in Hilbert spaces and/or where the data points are uncertain. In this context, 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 generalized to their robust counterpart in Banach spaces. These include the representer theorem, strong duality for the associated optimization problem as well as their geometrical interpretation. Furthermore, we propose a game theoretical interpretation of the class separation problem when the underlying space is reflexive and smooth. The proposed Nash equilibrium formulation draws connections and emphasizes the interplay between class separation in machine learning and game theory in the general setting of Banach spaces.