Robust SVM Optimization in Banach spaces

TL;DR

This paper extends classical SVM theory to Banach spaces, introducing robust optimization, duality, and geometric interpretations, along with a game-theoretic approach for convex set problems.

Contribution

It generalizes SVM results to Banach spaces, including robust formulations, duality, and geometric insights, and introduces a game-theoretic framework for convex set problems.

Findings

Generalization of SVM theory to Banach spaces

Development of a robust SVM formulation with duality

Game-theoretic interpretation for convex set problems

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.