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…
Comparing two probability distributions is a basic building block of statistics and machine learning, and the right family is well understood: the Rényi divergences of order $α\in[0,\infty]$ are the unique family monotone under data processing and additive on independent products…