On Sequences with Non-Learnable Subsequences
Abstract
The remarkable results of Foster and Vohra was a starting point for a series of papers which show that any sequence of outcomes can be learned (with no prior knowledge) using some universal randomized forecasting algorithm and forecast-dependent checking rules. We show that for the class of all computationally efficient outcome-forecast-based checking rules, this property is violated. Moreover, we present a probabilistic algorithm generating with probability close to one a sequence with a subsequence which simultaneously miscalibrates all partially weakly computable randomized forecasting algorithms. %subsequences non-learnable by each randomized algorithm. According to the Dawid's prequential framework we consider partial recursive randomized algorithms.
Cite
@article{arxiv.0806.4341,
title = {On Sequences with Non-Learnable Subsequences},
author = {Vladimir V. V'yugin},
journal= {arXiv preprint arXiv:0806.4341},
year = {2008}
}