The L2 penalty is a regularization term added to the loss function so as to induce coefficient shrinkage and does not yield to feature selection as mentioned in some of the comments (L1 penalty does this). It introduces bias to the regression and thus reduces its variance (bias-variance trade off).

1. Feature selection. 2. Prevent from overfitting(avoid high variance)

Sparse regression, the L2 penalty is a factor that controls bias va variance trade-off in a typical machine learning issue. It has nothing related to do Robustness/collinearity

Sparse regression, the L2 penalty is a factor that controls bias va variance trade-off in a typical machine learning issue. It has nothing related to do Robustness/collinearity