Vovk, Vladimir (2005) Competing with wild prediction rules.
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We consider the problem of on-line prediction competitive with a benchmarkclass 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.
This is a Submitted version This version's date is: 14/12/2005 This item is not peer reviewed
https://repository.royalholloway.ac.uk/items/9ce94366-2fbe-87cb-3995-afea82b135dd/1/
Deposited by Research Information System (atira) on 24-May-2012 in Royal Holloway Research Online.Last modified on 24-May-2012
28 pages, 3 figures