Adaptive Bayesian Online Learning via Expert Aggregation

2026-07-22

AI Summary

This work addresses the limitations of traditional Bayesian online learning, which relies on pre-specified inference components—such as priors, variational families, and learning rates—and struggles to adapt to dynamic data streams, thereby constraining predictive performance. The paper proposes the first adaptive Bayesian online learning framework based on expert aggregation, treating distinct Bayesian update rules as experts and dynamically combining them via weights determined by sequential prediction loss. The approach enables adaptation to unknown smoothness in Gaussian process regression and yields an oracle inequality for cumulative KL risk. By integrating online conformal inference, it also ensures valid stochastic coverage. Theoretically, the aggregated predictor is shown to compete with the best expert in hindsight, and experiments demonstrate that, without requiring prior knowledge, it effectively tracks strong experts and significantly enhances both predictive accuracy and robustness.

Abstract

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.

Problem

• Bayesian online learning
• expert aggregation
• adaptive inference
• uncertainty-aware prediction
• data streams

Innovation

• Adaptive Bayesian learning
• Expert aggregation
• Online conformal inference
• Gaussian process regression
• Oracle inequality