 The ideal goal is to select a function formula_12, where formula_13 is a space of functions called a hypothesis space, so that some notion of total loss is minimised.Depending on the type of model (statistical or adversarial), one can devise different notions of loss, which lead to different learning algorithms.In statistical learning models, the training sample formula_14 are assumed to have been drawn from the true distribution formula_4 and the objective is to minimize the expected "risk"
A common paradigm in this situation is to estimate a function formula_17 through empirical risk minimization or regularized empirical risk minimization (usually Tikhonov regularization).