Adaptive Bayes exactly tracks information over intrinsic time
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. Becaus...
| Authors | Akshay Balsubramani |
|---|---|
| Primary category | cs.LG |
| Published | 26 June 2026 |
| Last updated at source | 26 August 2026 |
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