Aggregating Algorithm competing with Banach lattices

TL;DR

This paper introduces a new online regression algorithm based on the Aggregating Algorithm that performs well on signals from Banach lattices and other complex function spaces, with broad applicability.

Contribution

It develops a semi-online prediction method that competes with linear functionals on Banach lattices and extends to arbitrary domains using Besov and Triebel-Lizorkin spaces.

Findings

Algorithm's cumulative loss is comparable to any linear functional on Banach lattices.

Extends to signals from arbitrary domains with loss comparable to predictors in advanced function spaces.

Applicable to various settings with signals in complex Banach and function spaces.

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.