|On the alpha-loss Landscape in the Logistic Model
|Tyler Sypherd, Arizona State University, United States; Mario Diaz, Universidad Nacional Autónoma de México, Mexico; Lalitha Sankar, Gautam Dasarathy, Arizona State University, United States
|L.9: Learning Methods and Networks
|Statistics and Learning Theory
|Click here to download the manuscript
|Click here to watch in the Virtual Symposium
|We analyze the optimization landscape of a recently introduced tunable class of loss functions called alpha-loss, alpha in (0,infinity], in the logistic model. This family encapsulates the exponential loss (alpha = 1/2), the log-loss (alpha = 1), and the 0-1 loss (alpha = infinity) 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 alpha-loss with respect to alpha 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.