Any Bayes/multiplicative-weights update has an exact regret identity that splits excess loss into an intrinsic-time uncertainty payment and KL transport to the comparator, for both retempered and local adaptive schedules.
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Adaptive Bayes exactly tracks information over intrinsic time
Any Bayes/multiplicative-weights update has an exact regret identity that splits excess loss into an intrinsic-time uncertainty payment and KL transport to the comparator, for both retempered and local adaptive schedules.