A Tunable Loss Function for Robust Classification: Calibration, Landscape, and Generalization

We introduce a tunable loss function called α-loss, parameterized by α ∈ (0,∞], which interpolates between the exponential loss (α = 1/2), the log-loss (α = 1), and the 0-1 loss (α = ∞), for the machine learning setting of classification. Theoretically, we illustrate a fundamental connection between α-loss and Arimoto conditional entropy, verify the classification-calibration of α-loss in order to demonstrate asymptotic optimality via Rademacher complexity generalization techniques, and build-upon a notion called strictly local quasi-convexity in order to quantitatively characterize the optimization landscape of α-loss. Practically, we perform class imbalance, robustness, and classification experiments on benchmark image datasets using convolutional-neural-networks. Our main practical conclusion is that certain tasks may benefit from tuning α-loss away from log-loss (α = 1), and to this end we provide simple heuristics for the practitioner. In particular, navigating the α hyperparameter can readily provide superior model robustness to label flips (α > 1) and sensitivity to imbalanced classes (α < 1).