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.

中文翻译：

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关于有偏见的随机游走、损坏的间隔和对抗性设计下的学习

我们解决了概率论中关于整数线上损坏的随机过程的一些基本问题。我们分析了何时有偏差的随机游走预计会到达其最低点，以及何时可以在自然噪声模型下检测到整数点的间隔。我们将这些结果应用于在对抗性设计下学习的新模型下的学习阈值和间隔问题。