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

Daniel Berend, Aryeh Kontorovich, Lev Reyzin, Thomas Robinson

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.