We study an instance of online non-parametric classification in the
realizable setting. In particular, we consider the classical 1-nearest neighbor
algorithm, and show that it achieves sublinear regret - that is, a vanishing
mistake rate - against dominated or smoothed adversaries in the realizable
setting.

研究在线非参数分类中的一个实例，并考虑经典的 1 最近邻算法，证明它在可实现设置中针对支配或平滑对手实现次线性遗憾 - 即消失的错误率。

在线最近邻分类

Online nearest neighbor classification

We study a recent model of collaborative PAC learning where $k$ players with
$k$ different tasks collaborate to learn a single classifier that works for all
tasks. Previous work showed that when there is a classifier that has very small
error on all tasks, there is a collaborative algorithm that finds a single
classifier for all tasks and has $O((\ln (k))^2)$ times the worst-case sample
complexity for learning a single task. In this work, we design new algorithms
for both the realizable and the non-realizable setting, having sample
complexity only $O(\ln (k))$ times the worst-case sample complexity for
learning a single task. The sample complexity upper bounds of our algorithms
match previous lower bounds and in some range of parameters are even better
than previous algorithms that are allowed to output different classifiers for
different tasks.

研究了一种近期的协作 PAC 学习模型，在这个模型下，k 个执行 k 个不同任务的参与者协作学习单个工作于所有任务的分类器。该研究设计了新算法，其中的样本复杂度仅为学习单个任务的最坏情况样本复杂度的 O (ln (k)) 倍，样本复杂度的上界与之前的算法匹配，并且在某些参数范围内甚至比允许输出不同分类器以适用于不同任务的先前算法更好。