New Smooth Loss functions for Robust Regression that Closely Approximate Absolute Error and Provide Improved Performance on Datasets With Significant Outliers

The paper introduces two new infinitely differentiable loss functions, Square Root Loss (SRL) and Smooth Mean Absolute Error (SMAE), designed to approximate Mean Absolute Error (MAE) while improving performance on regression tasks with significant outliers. The SRL loss is strictly convex, and SMAE is strictly quasi-convex, addressing the instability of MAE during training. These advancements are critical for practitioners as they enhance model robustness in the presence of outliers, potentially leading to more accurate regression outcomes across diverse datasets.