Objective function

An objective function $o: S \rightarrow E$ is simply a method to assess how “well” some function is doing. The evaluation space $E$ should ideally be totally ordered.

For example in the modelling framework given some testing data $T \subset A \times B$ the objective function could be Mean squared error (MSE) where $o: B^{T} \rightarrow \mathbb{R}_{\geq 0}$. Then $o((\hat{f}(a))_{(a, b) \in T})$ will be some score of candidate $\hat{f} \in M$. However, they can be much more generic or even less deterministic than this.