penalization

Penalization is the act or process of imposing a penalty as a consequence of violating rules or failing to meet obligations. In law and public policy, penalization describes the application of sanctions by a state or authorized body to punish or deter misconduct, protect the public, and promote compliance. Penalties may be criminal or civil and can take many forms, including fines, imprisonment, probation, restitution to victims, forfeiture of assets, or suspension or revocation of licenses and rights. The infliction of penalties is typically governed by a legal framework that defines offenses, procedures, and the principles of fairness, proportionality, and due process. Courts, regulatory agencies, and administrative bodies administer penalties, often considering intent, harm, and prior conduct.

In statistics and optimization, penalization refers to adding a penalty term to an objective function to constrain or regularize models or decisions. This technique discourages complexity or extreme parameter values and can improve generalization. Common penalization schemes include ridge (L2) regularization, LASSO (L1) regularization, and elastic net. Penalization is also used in constrained optimization to enforce bounds or penalties for constraint violations. The choice and magnitude of the penalty influence model bias and variance, and is often tuned on data through cross-validation or theoretical criteria.

Critically, penalization today raises questions about proportionality, equity, and unintended consequences in criminal justice, while in data contexts it requires careful selection to avoid underfitting or overfitting. In both senses, penalization is a mechanism to enforce norms by imposing costs or constraints.