Alternative loss functionIt is usually used when the loss function is inconvenient to calculate. If the proxy loss function is optimized, the original loss function is also optimized at the same time, that is, calibration or consistency, which is related to the original loss function.

If the alternative loss function is a convex function and is differentiable at point 0, then it is consistent when the derivative is less than 0, which is why a convex function is usually chosen as the loss function.

Common substitution functions

• Hinge loss: f ( x ) = max ( 0 , 1 - x )
• Exponential loss function: f ( x ) = exp ( – x )
• Logarithmic loss function: f ( x ) = log ( 1 + exp ( -x ))

Related terms: substitution function, loss function