The paper investigates how fast predictive regret guarantees of exact Bayesian online learning can be maintained when using approximate posterior methods. It establishes a general theorem linking the cumulative cost of posterior approximation to the contraction radius of the exact Gibbs posterior and the Wasserstein distance between approximate and exact posteriors. Three concrete online learning scenarios—linear models, infinite‑dimensional exponential families, and Gaussian process regression—illustrate that appropriately accurate approximations (projected Langevin, truncation, and sparse variational posteriors) preserve fast regret bounds while reducing computational demands.
By Ilsang Ohn
arXiv:2607. 12922v1 Announce Type: cross Abstract: Stochastic-process models are, as a rule, far easier to simulate than to condition.
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Stochastic-process models are, as a rule, far easier to simulate than to condition. Non-linear observations, non-Gaussian likelihoods, black-box information, and global constraints all induce intractable conditional laws, requiring bespoke, model-specific constructions.
arXiv:2511.20413v2 Announce Type: replace-cross
Abstract: \emph{Decision-focused learning} (DFL) trains predictive models to optimize downstream decisions rather than prediction accuracy alone. While...
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arXiv:2508.10336v3 Announce Type: replace-cross
Abstract: In a supervised online setting, quantifying uncertainty has been proposed in the seminal work of Gibbs and Cand\`es (2021). For any given poi...
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