CMP.7:4.4 - Give an effective selection or update procedure

Choose how data and feedback change the candidate:

Construction	Effective operation	Principal condition
Select from a finite family	Evaluate each rule on the relevant examples and select by the stated criterion, with an explicit treatment of ties.	The family and evaluations must be affordable.
Retain consistent candidates	Remove rules contradicted by newly observed feedback; use or combine the survivors.	Every observed label used for elimination must agree with one fixed target rule in the initial family.
Optimize a parameterized criterion	Construct updates or search using CMP.6 or CMP.4, including initialization, constraint handling and stopping.	Optimization progress and the meaning of the learning criterion both need their stated conditions.

For empirical risk minimization, a typical criterion is the average loss L_S(h)=(1/n)*sum loss(h(x_i),y_i). Regularization or another restriction can change the criterion. An argmin expression specifies the desired rule; the actual learner needs an obtaining procedure, including what it does when the minimum is not obtained or several rules tie.

Look for shared work and useful ordering. For thresholds, sorting examples once can let successive threshold scores be updated from counts rather than reevaluated on the whole dataset. CMP.3 supplies sharing when its identity conditions hold. For a parameterized learner, compare the work of one update, the updates needed and the later cost of applying the result.