Nonconvex Extension of Generalized Huber Loss for Robust Learning and Pseudo-Mode Statistics
This work addresses robust learning challenges in machine learning, but it appears incremental as it builds upon existing loss formulations.
The authors tackled the problem of robust learning by proposing an extended generalization of the pseudo Huber loss, which combines properties of strictly convex and robust loss functions, and they developed linear and exponential convergence algorithms for optimization.
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.