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arXiv · 1002.0709

Aggregating Algorithm competing with Banach lattices

Fedor Zhdanov·Alexey Chernov·Yuri Kalnishkan
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Abstract

The paper deals with on-line regression settings with signals belonging to a Banach lattice. Our algorithms work in a semi-online setting where all the inputs are known in advance and outcomes are unknown and given step by step. We apply the Aggregating Algorithm to construct a prediction method whose cumulative loss over all the input vectors is comparable with the cumulative loss of any linear functional on the Banach lattice. As a by-product we get an algorithm that takes signals from an arbitrary domain. Its cumulative loss is comparable with the cumulative loss of any predictor function from Besov and Triebel-Lizorkin spaces. We describe several applications of our setting.

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Fedor Zhdanov, Alexey Chernov, Yuri Kalnishkan. 2010-02-03. Aggregating Algorithm competing with Banach lattices. https://arxiv.org/abs/1002.0709

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