A note on supervised classification and Nash-equilibrium problems

Nicolas Couellan (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

In this note, we investigate connections between supervised classification and (Generalized) Nash equilibrium problems (NEP & GNEP). For the specific case of support vector machines (SVM), we exploit the geometric properties of class separation in the dual space to formulate a non-cooperative game. NEP and Generalized NEP formulations are proposed for both binary and multi-class SVM problems.

Mots clés: Supervised classification; support vector machine; multi-class SVM; Nash equilibrium; generalized Nash equilibrium; game theory

Domaines: Mathématiques [math]; Apprentissage [cs.LG]

Nicolas Couellan. A note on supervised classification and Nash-equilibrium problems. RAIRO - Operations Research, 2017, 51 (2), pp.329-341. ⟨10.1051/ro/2016024⟩. ⟨hal-01354857⟩