The Bayesian Learning Rule Beyond KL Geometry
The Bayesian learning rule (BLR) exploits the relation between Bayesian updating and the Kullback-Leibler divergence (KLD) to derive efficient additive updates for exponential family variational posteriors. The KL geometry is powerful but restrictive: combined with posterior families with parameter-dependent support it can lead to undefined objectives. We ask which non-KL geometries preserve the additive BLR computation. Previous works that use $f$-divergences suggest that this is only possible with the KLD. Here, we show that this is not true. We show that additive information-geometric optimization algorithms can be derived for the class of mixed-space Bregman or Fenchel-Young discrepan...
| Authors | Sophia Sklaviadis, Wu Lin, Andre Martins et al. |
|---|---|
| Primary category | cs.LG |
| Published | 22 October 2026 |
| Last updated at source | 22 October 2026 |
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