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On biased random walks, corrupted intervals, and learning under adversarial design

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Abstract

We tackle some fundamental problems in probability theory on corrupted random processes on the integer line. We analyze when a biased random walk is expected to reach its bottommost point and when intervals of integer points can be detected under a natural model of noise. We apply these results to problems in learning thresholds and intervals under a new model for learning under adversarial design.

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Acknowledgements

We thank an anonymous reviewer of a previous version of this paper for pointing us to the results that led to the discussion at the beginning of Section 4.4.

Daniel Berend was supported in part by the Milken Families Foundation Chair in Mathematics and the Cyber Security Research Center at Ben-Gurion University. Aryeh Kontorovich was supported in part by Israel Science Foundation grant 1602/19 and by Google Research. Lev Reyzin was supported in part by grants CCF-1934915 and CCF-1848966 from the National Science Foundation. Thomas Robinson was supported in part by Israeli Science Foundation grant 1002/14 and the Cyber Security Research Center at Ben-Gurion University

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Authors and Affiliations

  1. Ben-Gurion University, Be’er Sheva, Israel

    Daniel Berend, Aryeh Kontorovich & Thomas Robinson

  2. University of Illinois at Chicago, Chicago, IL, USA

    Lev Reyzin

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  1. Daniel Berend
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  2. Aryeh Kontorovich
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Correspondence to Lev Reyzin.

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Berend, D., Kontorovich, A., Reyzin, L. et al. On biased random walks, corrupted intervals, and learning under adversarial design. Ann Math Artif Intell 88, 887–905 (2020). https://doi.org/10.1007/s10472-020-09696-1

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