Fast rates in Bayesian online learning with approximate posteriors
Exact Bayes prediction enjoys fast predictive regret guarantees, but exact posterior updating or representation may be too costly for online use. We study when these statistical guarantees are preserved by computational approximations. We show that the cumulative price of posterior approximation can be governed by the interaction between the contraction radius of the exact Gibbs posterior and the Wasserstein distance between the approximate and exact posteriors. Our general theorem shows that whenever exact Bayes prediction achieves a fast regret bound, any approximate posterior method that tracks the exact posterior with sufficient accuracy inherits the same fast regret, up to an additiv...
| Authors | Ilsang Ohn |
|---|---|
| Primary category | stat.ML |
| Published | 26 August 2026 |
| Last updated at source | 26 August 2026 |
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