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Pac-bayesian inequalities for martingales (2012)
| Venue: | IEEE Transactions on Information Theory |
| Citations: | 14 - 4 self |
BibTeX
@ARTICLE{Seldin12pac-bayesianinequalities,
author = {Yevgeny Seldin and François Laviolette and Nicolò Cesa-bianchi and John Shawe-taylor and Peter Auer},
title = {Pac-bayesian inequalities for martingales},
journal = {IEEE Transactions on Information Theory},
year = {2012}
}
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Abstract
Abstract—We present a set of high-probability inequalities that control the concentration of weighted averages of multiple (possibly uncountably many) simultaneously evolving and interdependent martingales. Our results extend the PAC-Bayesian (probably approximately correct) analysis in learning theory from the i.i.d. setting to martingales opening the way for its application to importance weighted sampling, reinforcement learning, and other interactive learning domains, as well as many other domains in probability theory and statistics, where martingales are encountered. We also present a comparison inequality that bounds the expectation of a convex function of a martingaledifferencesequenceshiftedto the interval by the expectation of the same function of independent Bernoulli random variables. This inequality is applied to derive a tighter analog of Hoeffding–Azuma’s inequality. Index Terms—Bernstein’s inequality, Hoeffding–Azuma’s inequality, martingales, PAC-Bayesian bounds.
Keyphrases
pac-bayesian inequality hoeffding azuma inequality high-probability inequality many domain independent bernoulli random variable comparison inequality weighted average reinforcement learning weighted sampling interdependent martingale interactive learning domain probability theory pac-bayesian bound convex function index term bernstein inequality
