竞争在线预测中的领先策略
Leading strategies in competitive on-line prediction
摘要：
我们从二次损失函数的在线回归问题的一个简单的渐近结果开始：连续有限记忆预测策略类允许“领先预测策略”，其不仅渐近地执行至少与任何连续有限存储器策略一样好，而且还满足任何连续有限存储器策略的过度损失的性质，记忆策略取决于它模仿领先策略的程度。更具体地说，对于构成再生核希尔伯特空间的任何一类预测策略，我们构造一个领先策略，在这个意义上，任何预测策略的损失，其范数不是太大，是由它模仿领先策略的程度决定的。这个结果被推广到由Bregman分歧和严格适当的评分规则给出的损失函数。
英文摘要：
We start from a simple asymptotic result for the problem of on-line regression with the quadratic loss function: the class of continuous limited-memory prediction strategies admits a "leading prediction strategy", which not only asymptotically performs at least as well as any continuous limited-memory strategy but also satisfies the property that the excess loss of any continuous limited-memory strategy is determined by how closely it imitates the leading strategy. More specifically, for any class of prediction strategies constituting a reproducing kernel Hilbert space we construct a leading strategy, in the sense that the loss of any prediction strategy whose norm is not too large is determined by how closely it imitates the leading strategy. This result is extended to the loss functions given by Bregman divergences and by strictly proper scoring rules.
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