On the α-loss Landscape in the Logistic Model

Abstract

We analyze the optimization landscape of a recently introduced tunable class of loss functions called α-loss, α ∈ (0, ∞], in the logistic model. This family encapsulates the exponential loss (α = 1/2), the log-loss (α = 1), and the 0-1 loss (α = ∞) and contains compelling properties that enable the practitioner to discern among a host of operating conditions relevant to emerging learning methods. Specifically, we study the evolution of the optimization landscape of α-loss with respect to α using tools drawn from the study of strictly-locally-quasi-convex functions in addition to geometric techniques. We interpret these results in terms of optimization complexity via normalized gradient descent.