2005/12/14 by Vladimir Vovk, Vovk, Vladimir · 1 citation
Computer Science · Decision Sciences · #Advanced Bandit Algorithms Research #FOS: Computer and information sciences #I.2.6 #Machine Learning (cs.LG) #Machine Learning and Algorithms #Reinforcement Learning in Robotics #cs.LG
paper · pdf · doi:10.48550/arxiv.cs/0512059
28 pages, 3 figures
openalex publication_date 2005/12/14 · arxiv created 2006/01/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.