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PAC-Bayes-Bernstein Inequality for Martingales and its Application to Multiarmed Bandits

2012

Conference Paper

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We develop a new tool for data-dependent analysis of the exploration-exploitation trade-off in learning under limited feedback. Our tool is based on two main ingredients. The first ingredient is a new concentration inequality that makes it possible to control the concentration of weighted averages of multiple (possibly uncountably many) simultaneously evolving and interdependent martingales. The second ingredient is an application of this inequality to the exploration-exploitation trade-off via importance weighted sampling. We apply the new tool to the stochastic multiarmed bandit problem, however, the main importance of this paper is the development and understanding of the new tool rather than improvement of existing algorithms for stochastic multiarmed bandits. In the follow-up work we demonstrate that the new tool can improve over state-of-the-art in structurally richer problems, such as stochastic multiarmed bandits with side information (Seldin et al., 2011a).

Author(s): Seldin, Y. and Cesa-Bianchi, N. and Auer, P. and Laviolette, F. and Shawe-Taylor, J.
Book Title: JMLR Workshop and Conference Proceedings 26
Pages: 98-111
Year: 2012
Month: April
Day: 0
Publisher: JMLR

Department(s): Empirical Inference
Bibtex Type: Conference Paper (inproceedings)

Event Name: On-line Trading of Exploration and Exploitation 2
Event Place: Bellevue, WA, USA

Address: Cambridge, MA, USA
Digital: 0

Links: PDF
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BibTex

@inproceedings{SeldinCALS2011,
  title = {PAC-Bayes-Bernstein Inequality for Martingales and its Application to Multiarmed Bandits},
  author = {Seldin, Y. and Cesa-Bianchi, N. and Auer, P. and Laviolette, F. and Shawe-Taylor, J.},
  booktitle = {JMLR Workshop and Conference Proceedings 26},
  pages = {98-111},
  publisher = {JMLR},
  address = {Cambridge, MA, USA},
  month = apr,
  year = {2012},
  month_numeric = {4}
}