与野生预测规则竞争
Competing with wild prediction rules
摘要：
我们认为在线预测的问题与基准类的连续，但高度不规则的预测规则的竞争。已知如果基准类是再生核希尔伯特空间，则存在预测算法，其在前N个示例上的平均损失不超过该类中任何预测规则的平均损失加上O（N^（-1/2））的“遗憾项”。然而，一些自然基准类的元素是如此不规则，以至于这些类不是希尔伯特空间。在本文中，我们开发了Banach空间方法来构造一个预测算法，其后悔项为O（N^（-1/p）），其中p在[2，infty]中，p-2反映了基准类不能成为Hilbert空间的程度。
英文摘要：
We consider the problem of on-line prediction competitive with a benchmark class of continuous but highly irregular prediction rules. It is known that if the benchmark class is a reproducing kernel Hilbert space, there exists a prediction algorithm whose average loss over the first N examples does not exceed the average loss of any prediction rule in the class plus a "regret term" of O(N^(-1/2)). The elements of some natural benchmark classes, however, are so irregular that these classes are not Hilbert spaces. In this paper we develop Banach-space methods to construct a prediction algorithm with a regret term of O(N^(-1/p)), where p is in [2,infty) and p-2 reflects the degree to which the benchmark class fails to be a Hilbert space.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
