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== Generalized Smooth Hinge loss ==
The generalized smooth hinge loss function with parameter <math>\alpha</math> is defined as
:<math>f^*_\alpha(z) \;=\; \begin{cases} \frac{\alpha}{\alpha + 1}& \text{if }z< 0 \\ \frac{1}{\alpha + 1}z^{\alpha + 1} - z + \frac{\alpha}{\alpha + 1} & \text{if } 0<z<1 \\ 0 & \text{if } z \geq 1 \end{cases}.</math>
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It is monotonically increasing and reaches 0 when :<math>z = 1</math>
== Logistic loss ==
The logistic loss function is defined as
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