PAC-Bayesian Inequalities for Martingales

Seldin, Y; Laviolette, F; Cesa-Bianchi, N; Shawe-Taylor, J; Auer, P

doi:10.1109/TIT.2012.2211334

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PAC-Bayesian Inequalities for Martingales

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Seldin, Y
Dept. Empirical Inference, Max Planck Institute for Intelligent Systems, Max Planck Society;

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Citation

Seldin, Y., Laviolette, F., Cesa-Bianchi, N., Shawe-Taylor, J., & Auer, P. (2012). PAC-Bayesian Inequalities for Martingales. IEEE Transactions on Information Theory, 58(12), 7086-7093. doi:10.1109/TIT.2012.2211334.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-B544-8

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. We also present a comparison inequality that bounds expectation of a convex function of martingale difference type variables by expectation of the same function of independent Bernoulli variables. This inequality is applied to derive a tighter analog of Hoeffding-Azuma inequality.