Competing with wild prediction rules
<|reference_start|>Competing with wild prediction rules: 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.<|reference_end|>
@article{vovk2005competing,
    title={Competing with wild prediction rules},
    author={Vladimir Vovk},
    journal={arXiv preprint arXiv:cs/0512059},
    year={2005},
    archivePrefix={arXiv},
    eprint={cs/0512059},
    primaryClass={cs.LG}
}