A KL-centroid optimization problem leads to a closed-form solution with Lambert W
FrnkNlsn · x · 2026-08-04
The post describes a variational optimization problem: finding a distribution r that minimizes DKL[p:r] + DKL[r:q]. The solution is expressed with the Lambert W function, and the unique normalizing constant λ is what makes r a valid probability distribution.
It also notes that this appears in Jeffreys centroids and symmetrized Bregman centroids.
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