L0 Norm Regularization

L0 norm regularization is a form of penalty that counts the number of non-zero coefficients in a model. It explicitly encourages the model to use the fewest number of features possible, which is the purest form of sparsity.

While theoretically ideal, L0 regularization is computationally difficult to solve because it involves a discrete optimization problem. In practice, L1 regularization is often used as a convex approximation to L0.

It is the gold standard for model simplicity, as it forces the algorithm to select only the most essential predictors. This approach is highly valued in fields where interpretability and computational efficiency are paramount.

It represents the ultimate goal of model parsimony.