by **G. Kerkyacharian, A. B. Tsybakov, V. Temlyakov, D. Picard & V. Koltchinskii**

Consider a standard binary classification problem, in which *(X, Y)* is a random couple in *X* ×*{0, 1}*, and the training data consist of *n* i.i.d. copies of *(X, Y)*. Given a binary classifier *f* : *X* *→ {0, 1}*, the generalization error of f is defined by R( f ) = P{Y = f (X)}. Its minimum R∗ over all binary classifiers f is called the Bayes risk and is attained at aBayes classifier. The performance of any binary classifier fˆn based on the training data is characterized by the excess risk *R(fn) − R***∗*.We study Bahadur’s type exponential bounds on the following minimax accuracy confidence function based on the excess risk: (…)