Convex Loss Function

A Convex Loss Function is a loss function that is a convex function.

• Context:
  • It can be an input to a Convex Optimization Task.
  • …
• Example(s):
  • Hinge Loss, which is non-differentiable.
  • Log Loss.
  • …
• Counter-Example(s):
  • …
• See: Bounded Loss Function, 0-1 Loss Function.

---

---

References

2014

• http://scikit-learn.org/0.11/modules/sgd.html
  • Stochastic Gradient Descent (SGD) is a simple yet very efficient approach to discriminative learning of linear classifiers under convex loss functions such as (linear) Support Vector Machines and Logistic Regression.

2009

• (Gentle, 2009) ⇒ James E. Gentle. (2009). “Computational Statistics." Springer. ISBN:978-0-387-98143-7
  • QUOTE: Any strictly convex loss function over an unbounded interval is unbounded. It is not always realistic to use an unbounded loss function. A common bounded loss function is the 0-1 loss function, which may be …

---