A Tunable Loss Function for Binary Classification

We prove that α-loss has an equivalent margin-based form and is classification-calibrated, two desirable properties for a good surrogate loss function for the ideal yet intractable 0-1 loss. For logistic regression-based classification, we provide an upper bound on the difference between the empirical and expected risk for α-loss by exploiting its Lipschitzianity along with recent results on the landscape features of empirical risk functions. Finally, we show that α-loss with α 2 performs better than log-loss on MNIST for logistic regression. I. INTRODUCTION In learning theory, the performance of a classification algorithm interms of accuracy, tractability, and convergence guarantees is contingent on the choice of a loss function. Consider a feature vector X X, an unknown finite label Y Y, and a hypothesis test h: X Y. The canonical 0-1 loss, given by 1[h(X) Y ], is considered an ideal loss function that captures the probability of incorrectly guessing the true label Y using h(X).