Convex function

A function in which the region above the graph of the function is a convex set. The prototypical convex function is shaped something like the letter U.¹

Strictly convex function

A strictly convex function has exactly one local minimum point, which is also the global minimum point. The classic U-shaped functions are strictly convex functions. However, some convex functions (for example, straight lines) are not U-shaped.¹

Examples

A lot of the common loss functions, including the following, are convex functions:¹

• L2 loss
• Log loss
• L1 regularization
• L2 regularization

See also

• Gradient descent: Many variations of gradient descent are guaranteed to find a point close to the minimum of a strictly convex function.
• Stochastic gradient descent: Many variations of stochastic gradient descent have a high probability of finding a point close to the minimum of a strictly convex function.

Footnotes

1. developers.google.com/machine-learning/glossary#convex-function ↩ ↩² ↩³