Epsilon-insensitive loss

The problem, from first principles

Hinge loss lets a classifier ignore any point that is comfortably on the right side of the margin. Regression needs the same idea with a different shape: a prediction that lands within epsilon of the true value should cost nothing, and a prediction outside that tube should be charged only for the distance beyond its edge. This is the epsilon-insensitive loss, the loss behind Support Vector Regression.

Given predictions and targets of the same shape, return max(0, |prediction - target| - epsilon) for each pair, then reduce it.

Constraints

• reduction is "mean" (default), "sum", or "none". Any other value raises ValueError.
• epsilon defaults to 0.1.
• A residual exactly equal to epsilon costs 0.
• Do not modify the inputs.

Hints

Open one at a time. Each gives away a little more than the last.