aiqbench analysis
This research establishes an exact information-accounting identity for Bayesian and multiplicative-weights updates, linking cumulative regret directly to a pathwise "intrinsic time" metric. By deriving adaptive decompositions that hold across diverse online-learning settings—from contextual bandits to repeated games—the study provides a unified theoretical framework where learning rates naturally scale with the inverse square root of this intrinsic uncertainty clock. The findings offer significant theoretical clarity for understanding how stochastic regimes and noise levels self-bound within these fundamental algorithms without requiring heuristic adjustments.
Adaptive Bayes exactly tracks information over intrinsic time
arXiv:2607.08789v2 Announce Type: replace Abstract: Bayesian and multiplicative-weights updates reweight experts, models, or actions from sequential feedback. We show that the regret of any such update obeys an exact information-accounting identity. On each round, the learner's excess loss to any chosen comparator is the sum of an immediate cost for the uncertainty exposed by the round and a reduction in the information distance from the learner's current weights to the comparator. The cumulative cost defines a pathwise uncertainty clock, the intrinsic time of the realized sequence. Summing one-step balances yields two exact adaptive decompositions of cumulative regret, one for each natural way of composing the update across rounds. Because the decompositions are exact, favorable stochastic or low-noise regimes appear as self-bounding properties of the realized intrinsic time. The accounting also fixes a learning rate, inverse in the square root of intrinsic time. That schedule is competitive with adaptive baselines in selected online-learning settings. The same calculus covers Hedge, optimistic and side-information variants, continuous priors, boosting, online convex optimization, contextual bandits, and repeated games: the pathwise account is the same in every case.
Abstract:Bayesian and multiplicative-weights updates reweight experts, models, or actions from sequential feedback. We show that the regret of any such update obeys an exact information-accounting identity. On each round, the learner's excess loss to any chosen comparator is the sum of an immediate cost for the uncertainty exposed by the round and a reduction in the information distance from the learner's current weights to the comparator. The cumulative cost defines a pathwise uncertainty clock, the intrinsic time of the realized sequence. Summing one-step balances yields two exact adaptive decompositions of cumulative regret, one for each natural way of composing the update across rounds. Because the decompositions are exact, favorable stochastic or low-noise regimes appear as self-bounding properties of the realized intrinsic time. The accounting also fixes a learning rate, inverse in the square root of intrinsic time. That schedule is competitive with adaptive baselines in selected online-learning settings. The same calculus covers Hedge, optimistic and side-information variants, continuous priors, boosting, online convex optimization, contextual bandits, and repeated games: the pathwise account is the same in every case.
Machine Learning (cs.LG); Information Theory (cs.IT); Statistics Theory (math.ST); Machine Learning (stat.ML)
arXiv:2607.08789 [cs.LG]
(or arXiv:2607.08789v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2607.08789 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 278 words
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