Exponential convergence of testing error for stochastic gradient methods

Loucas Pillaud-Vivien (1) , Alessandro Rudi (1) , Francis Bach (1)

1 SIERRA - Statistical Machine Learning and Parsimony

We consider binary classification problems with positive definite kernels and square loss, and study the convergence rates of stochastic gradient methods. We show that while the excess testing loss (squared loss) converges slowly to zero as the number of observations (and thus iterations) goes to infinity, the testing error (classification error) converges exponentially fast if low-noise conditions are assumed.

Mots clés: binary classification; margin condition; positive-definite kernels; SGD

Domaines: Apprentissage [cs.LG]; Autres [stat.ML]

Loucas Pillaud-Vivien, Alessandro Rudi, Francis Bach. Exponential convergence of testing error for stochastic gradient methods. Conference on Learning Theory (COLT), Jul 2018, Stockholm, Sweden. ⟨hal-01662278v3⟩