The cost of useful natural gradient updates
What information is needed to turn a natural-gradient direction into a useful finite update? Under a population Kullback-Leibler (KL) budget, we call a step useful if it is feasible and loses at most a fraction $\varepsilon$ of the best feasible gain along the direction. We construct a four-state exponential family whose laws share their initial gradient, scalar Fisher information and natural gradient, yet two laws have disjoint useful-step sets. With these quantities supplied exactly and the law otherwise known only through draws, the family's worst-case sample complexity is $Θ(\log(1/δ)/(p\varepsilon^2))$ for small $\varepsilon$, where $p$ scales rare-state probabilities and $δ$ is the ...
| Authors | Subhransu S. Bhattacharjee, Dylan Campbell, Rahul Shome |
|---|---|
| Primary category | cs.LG |
| Published | 27 September 2026 |
| Last updated at source | 27 September 2026 |
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