Differences between L1 and L2 as Loss Function and Regularization

Next time I will not draw mspaint but actually plot it out.] While practicing machine learning, you may have come upon a choice of the mysterious L1 vs L2. Usually the two decisions are: 1) L1-norm vs L2-norm loss function; and 2) L1-regularization vs L2-regularization. L1-norm loss function is also known as least absolute deviations (LAD), least absolute errors (LAE). L2-norm loss function is also known as least squares error (LSE). The method of least absolute deviations finds applications in many areas, due to its robustness compared to the least squares method. Least absolute deviations is robust in that it is resistant to outliers in the data.