标题： 带有应用的博弈论模式估计的鲁棒性保证 显示英文标题

标题： Robustness Guarantees for Mode Estimation with an Application to Bandits

摘要： 模式估计是统计学中的一个经典问题，在机器学习中有广泛的应用。尽管如此，对于在可能的对抗性数据污染下的鲁棒性特性，了解仍然有限。在本文中，我们在简单的随机化下给出了精确的鲁棒性保证以及隐私保证。然后，我们引入了一个多臂老虎机理论，其中值是奖励分布的模式而不是均值。我们证明了顶级臂识别、顶级m臂识别、上下文模式老虎机和无限连续臂顶级臂恢复问题的遗憾保证。我们在模拟中展示了我们的算法对由对抗性噪声序列引起的臂的扰动具有鲁棒性，因此使得模式老虎机在奖励可能包含异常值或对抗性破坏的情况下成为一个有吸引力的选择。 显示英文摘要

摘要： Mode estimation is a classical problem in statistics with a wide range of applications in machine learning. Despite this, there is little understanding in its robustness properties under possibly adversarial data contamination. In this paper, we give precise robustness guarantees as well as privacy guarantees under simple randomization. We then introduce a theory for multi-armed bandits where the values are the modes of the reward distributions instead of the mean. We prove regret guarantees for the problems of top arm identification, top m-arms identification, contextual modal bandits, and infinite continuous arms top arm recovery. We show in simulations that our algorithms are robust to perturbation of the arms by adversarial noise sequences, thus rendering modal bandits an attractive choice in situations where the rewards may have outliers or adversarial corruptions.