PAC-Bayes Iterated Logarithm Bounds for Martingale Mixtures

06/22/2015

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by   Akshay Balsubramani, et al.

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We give tight concentration bounds for mixtures of martingales that are simultaneously uniform over (a) mixture distributions, in a PAC-Bayes sense; and (b) all finite times. These bounds are proved in terms of the martingale variance, extending classical Bernstein inequalities, and sharpening and simplifying prior work.