On the alpha-loss Landscape in the Logistic Model

06/22/2020

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by   Tyler Sypherd, et al.

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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.