Bregman divergence

In mathematics, a Bregman divergence or Bregman distance is similar to a metric, but does not satisfy the triangle inequality nor symmetry.

Bregman divergences are named after Lev M. Bregman, who introduced the concept in 1967.

Let ${\displaystyle F:\Omega \to \mathbb {R} }$ be a continuously-differentiable real-valued and strictly convex function defined on a closed convex set ${\displaystyle \Omega }$.

The Bregman distance associated with F for points ${\displaystyle p,q\in \Omega }$ is the difference between the value of F at point p and the value of the first-order Taylor expansion of F around point q evaluated at point p:

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