Abstract
It is well known that there exists a universal (i.e., optimal to within an additive constant if allowed to work infinitely long) algorithm for lossless data compression (Kolmogorov, Levin). The game of lossless compression is an example of an on-line prediction game; for some other on-line prediction games (such as the simple prediction game) a universal algorithm is known not to exist. In this paper we give an analytic characterisation of those binary on-line prediction games for which a universal prediction algorithm exists.
A version of this paper with more details is available as Technical Report CLRC-TR-04-04 (revised), Computer Learning Research Centre, Royal Holloway, University of London; see http://www.clrc.rhul.ac.uk/publications/techrep.htm
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Kalnishkan, Y., Vovk, V., Vyugin, M.V. (2004). A Criterion for the Existence of Predictive Complexity for Binary Games. In: Ben-David, S., Case, J., Maruoka, A. (eds) Algorithmic Learning Theory. ALT 2004. Lecture Notes in Computer Science(), vol 3244. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30215-5_20
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DOI: https://doi.org/10.1007/978-3-540-30215-5_20
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