Huber Loss

Definition

Huber loss is a Loss Function used in robust regression, that is less sensitive to outliers in data than the Squared Error Loss. It is quadratic within $\delta$-radius and linear on the outside. $L_{\delta }(x)=\{\begin{array}{ll}\frac{1}{2}{x}^2& |x|\le \delta \\ \delta |x|-\frac{1}{2}{\delta }^2& \text{otherwise}\end{array}$

Huber loss is also as differentiable alternative to the absolute value function.