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We propose an extended generalization of the pseudo Huber loss formulation.We show that using the log-exp transform together with the logistic function,we can create a loss which combines the desirable properties of the strictlyconvex losses with robust loss functions. With this formulation, we show that alinear convergence algorithm can be utilized to find a minimizer. We furtherdiscuss the creation of a quasi-convex composite loss and provide aderivative-free exponential convergence rate algorithm.

Nonconvex Extension of Generalized Huber Loss for Robust Learning and Pseudo-Mode Statistics