where X denotes an instance space, and Y represents the corresponding set of outcomes. The training instances are assumed to be independent and identically distributed according to some unknown probability measure P on X × Y, with density function p. Given a hypothesis space H containing hypotheses h : X → Y mapping and instance x to an outcome y and a loss function L : Y × Y → R, the objective is to find a hypothesis h ⋆ ∈ H that minimizes the expected loss :