  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 strictly
convex losses with robust loss functions. With this formulation, we show that a
linear convergence algorithm can be utilized to find a minimizer. We further
discuss the creation of a quasi-convex composite loss and provide a
derivative-free exponential convergence rate algorithm.
