Huber Loss

$$L_{\delta }(y,\hat{y})=\{\begin{array}{ll}\frac{1}{2}(y-\hat{y}{)}^2& \text{if }|y-\hat{y}|\le \delta \\ \delta |y-\hat{y}|-\frac{1}{2}{\delta }^2& \text{otherwise}\end{array}$$

Characteristics:

• Quadratic for small errors (like L2), linear for large errors (like L1).
• Balances robustness and smooth optimization.
• Common in regression tasks where outliers may exist.