Adaptive Bayesian Online Learning via Expert Aggregation

Source

Source name: arXiv
Source kind: paper
Authors / organization: Jungbin Jun, Ilsang Ohn
Venue: arXiv: stat.ML
Published: 2026-07-22
Collected: 2026-07-23
URL: http://arxiv.org/abs/2607.20239v1
PDF: https://arxiv.org/pdf/2607.20239v1
DOI: UNKNOWN

Plain-Language Brief

The researchers propose a method for Bayesian online learning that allows for uncertainty-aware predictions on data streams. Instead of fixing inferential choices before seeing the stream, they treat update rules as 'experts' and aggregate these experts based on sequential predictive losses. The proposed approach competes with the best expert in hindsight at an aggregation cost determined by how each expert's per-round performance is evaluated. The method is applied to online conformal inference and Gaussian process regression, leading to improved results in experiments.

What the Document Says

The paper presents a method for Bayesian online learning where inferential choices are treated as experts and aggregated based on sequential predictive losses.
They prove that the aggregate competes with the best expert in hindsight at an aggregation cost determined by each expert's per-round performance evaluation.
The framework is instantiated for online conformal inference and Gaussian process regression.
In online conformal inference, a smoothed Bayesian counterpart of adaptive conformal inference with long-run randomized coverage is achieved.
In Gaussian process regression, an oracle inequality in cumulative predictive Kullback-Leibler risk and adaptation to unknown Hölder smoothness up to logarithmic factors are obtained.

Key Concepts Mentioned

Bayesian online learning
expert aggregation
inferential choices
learning rates
prior distributions
variational families
sequential predictive losses
online conformal inference
Gaussian process regression
Hölder smoothness

Claims Made by the Document

The proposed method competes with the best expert in hindsight.
The approach adapts to unknown Hölder smoothness up to logarithmic factors.

Evidence Used

They provide a theoretical proof for the first claim.
In the Gaussian process application, they state that an oracle inequality in cumulative predictive Kullback-Leibler risk is obtained, which implies the second claim.

Methods / Approach

UNKNOWN

Limitations Stated by the Authors

UNKNOWN

Limitations Noted by the Agent

Agent interpretation — not from the source.

UNKNOWN

Open Questions

UNKNOWN

Notes for Future Q&A

May include interpretation. Labeled where it does.

UNKNOWN

Raw Abstract / Excerpt

Bayesian online learning promises uncertainty-aware prediction on data streams, but its performance hinges on inferential choices, including learning rates, prior distributions and variational families, which are usually fixed before seeing the stream. We address this by treating Bayesian update rules as experts and aggregating the Bayesian experts according to sequential predictive losses. We prove that the resulting aggregate competes with the best expert in hindsight at an aggregation cost determined by how each expert's per-round performance is evaluated. We instantiate the framework in online conformal inference and Gaussian process regression. The conformal inference application yields a smoothed Bayesian counterpart of adaptive conformal inference with long-run randomized coverage, while the Gaussian process application gives an oracle inequality in cumulative predictive Kullback-Leibler risk and adaptation to unknown Hölder smoothness up to logarithmic factors. Experiments show that the aggregate tracks strong experts without oracle expert selection.