Bregman divergence

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A Bregman divergence is similar to a metric, but does not satisfy the triangle inequality.

More formally if F: \Delta \to \Re is a continuously-differentiable real-valued and strictly convex function defined on a closed convex set Δ, then the Bregman distance associated for with F for points p, q \in \Delta is:

B_F(p \rVert q) = F(p)-F(q)-\nabla F(q) \cdot (p-q)

Intuitively this can be thought of as 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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