My answer has to do with the loss function that you have.

Various loss functions appropriate for different tasks may be used there.

It is important for the loss function to be convex.

The training set error can be calculated with different loss functions.

In statistics, decision theory, and some economic models, a loss function plays a similar role.

Let us consider the setting of supervised learning with the square loss function.

However, if the parameter were to be moved into a completely different place, the loss function may actually become smaller.

The particular loss function depends on the type of label being predicted.

It will then use this information to follow a path towards the minimum of the loss function.

The choice of a loss function is not arbitrary.

The first two cases are represented by simple monotonic loss functions.

This chapter concerns inference alone and no loss functions are involved.

That is, minimize the expected risk for a Least-squares loss function.

Hence, solutions to where is some empirical loss function, need not be unique.

Note also that in practice when the loss function is differentiable at the origin.

This familiar loss function is used in ordinary least squares regression.

Phrased in this manner, there is no reason why you cannot consider other loss functions.

There is a lot of flexibility allowed in the choice of loss function.

In an inference context the loss function would take the form of a scoring rule.

The loss function also affects the convergence rate for an algorithm.

The problem is more complex when the loss function includes more than two objectives.

Stein's result has been extended to a wide class of distributions and loss functions.

The use of a quadratic loss function is common, for example when using least squares techniques.

However, in some circumstances, the estimation will "get stuck," and as a result, you would see a very large value of the loss function.

Since is a constant, it can be taken out of the expected loss function (this is only true if ).