PAC-Bayes Iterated Logarithm Bounds for Martingale Mixtures
This provides incremental theoretical improvements in concentration inequalities for martingales, relevant for researchers in probability theory and machine learning.
The paper tackles the problem of deriving tight concentration bounds for mixtures of martingales that are uniform over mixture distributions and all finite times, resulting in bounds expressed in terms of martingale variance that extend classical Bernstein inequalities and improve prior work.
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.