L1 Loss

$L_1=\frac{1}{N}{\sum }_{i=1}^N\left|y_i-{\hat{y}}_i\right|$

• Intuition: Measures the average absolute difference between predicted and true values.
• Characteristics:
  • Produces a linear penalty → every unit of error is penalized equally.
  • More robust to outliers, since large errors don’t get squared.
  • Optimization is harder because the absolute function is not differentiable at 0 (though subgradients are used).