Adaptive Bayes exactly tracks information over intrinsic time

2026-05-24 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences · Depth: Expert, extended

Summary

Adaptive Bayes updates, encompassing Bayesian and multiplicative-weights methods, are shown to obey an exact information-accounting identity. This framework introduces "intrinsic time," a pathwise uncertainty clock, which quantifies the cumulative payment for uncertainty exposed by a realized sequence. The paper presents two exact adaptive decompositions of cumulative regret: one for a prior-retempered update and another for a local update. This calculus applies broadly, covering algorithms like Hedge, boosting, online convex optimization, contextual bandits, and reinforcement learning from human feedback. The approach reveals how information is spent and gained, offering a precise, rather than approximate, understanding of regret.

Key takeaway

For research scientists developing or applying online learning algorithms, you should adopt this exact information-accounting framework to precisely understand regret. This allows you to differentiate whether performance stems from inherent sequence difficulty, comparator complexity, or schedule-induced distortion. By using intrinsic time, you can design more robust adaptive learning rates and interpret algorithm behavior beyond worst-case bounds.

Key insights

Bayesian and multiplicative updates' regret is exactly accounted for by an information identity and intrinsic time.

Principles

• Regret splits into immediate uncertainty payment.
• Information measures comparator complexity and sequence difficulty.

Method

Two adaptive updates: prior-retempered (recomputes posterior from prior) and local (updates from current weights). Schedules include square-root clock and pressure-target line search.

In practice

• Apply to Bayesian model averaging and bandit algorithms.
• Use in boosting, online convex optimization, and RLHF.

Topics

• Bayesian Online Learning
• Multiplicative Weights Update
• Regret Analysis
• Intrinsic Time
• Adaptive Learning Rates
• Online Convex Optimization
• Contextual Bandits

Best for: AI Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.