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This paper proves that unbounded gaps between update maps can coexist with vanishing predictive KL divergence in stationary symmetric Gaussian HMMs, showing that internal computational mismatches do not necessarily imply predictive failure.
This paper demonstrates that the regret of Bayesian and multiplicative-weights updates satisfies an exact information-accounting identity, decomposing the learner's excess loss into an uncertainty payment and a reduction in information distance to any comparator. The cumulative payment defines intrinsic time, leading to exact adaptive regret decompositions that unify Hedge, Bayesian model averaging, online convex optimization, and other algorithms.