#huber-loss

The Huber loss with threshold $\sigma$ is $l(r) = \frac{r^2}{2\sigma}$ for $|r| \le \sigma$ and $l(r) = |r| - \frac{\sigma}{2}$ otherwise, where $r = \hat y - y$ is the residual. With $\sigma = 2$, the derivative $dl/dr$ is for a residual $r = 1.5$ and for an outlier with $r = 500$.