@inproceedings{d2528a076ea14268a1cdb6e8f1a45ebe,
title = "Indefinitely oscillating martingales",
abstract = "We construct a class of nonnegative martingale processes that oscillate indefinitely with high probability. For these processes, we state a uniform rate of the number of oscillations for a given magnitude and show that this rate is asymptotically close to the theoretical upper bound. These bounds on probability and expectation of the number of upcrossings are compared to classical bounds from the martingale literature. We discuss two applications. First, our results imply that the limit of the minimum description length operator may not exist. Second, we give bounds on how often one can change one{\textquoteright}s belief in a given hypothesis when observing a stream of data.",
keywords = "Bounds, Convergence rates, Infinite oscillations, Martingales, Mind changes, Minimum description length",
author = "Jan Leike and Marcus Hutter",
note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2014.; 25th International Conference on Algorithmic Learning Theory, ALT 2014 ; Conference date: 08-10-2014 Through 10-10-2014",
year = "2014",
doi = "10.1007/978-3-319-11662-4_23",
language = "English",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "321--335",
editor = "Peter Auer and Alexander Clark and Thomas Zeugmann and Sandra Zilles",
booktitle = "Algorithmic Learning Theory - 25th International Conference, ALT 2014, Proceedings",
address = "Germany",
}