### Abstract

We bound the future loss when predicting any (computably) stochastic sequence online. Solomonoff finitely bounded the total deviation of his universal predictor M from the true distribution m by the algorithmic complexity of m. Here we assume we are at a time t>1 and already observed x=x 1...xt. We bound the future prediction performance on xt+1xt+2... by a new variant of algorithmic complexity of m given x, plus the complexity of the randomness deficiency of x. The new complexity is monotone in its condition in the sense that this complexity can only decrease if the condition is prolonged. We also briefly discuss potential generalizations to Bayesian model classes and to classification problems.

Original language | English |
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Title of host publication | Proceedings of the 16th International Conference Algorithmic Learning Theory 2005 |

Place of Publication | Berlin Heidelberg |

Publisher | Springer |

Pages | 414-428 |

Number of pages | 15 |

Volume | 3734 |

DOIs | |

Publication status | Published - 31 Dec 2005 |

Event | Proceedings of the 16th International Conference Algorithmic Learning Theory 2005 - Singapore, October 8-11, 2005 Duration: 31 Dec 2005 → … |

### Publication series

Name | Lecture Notes in Computer Science |
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### Conference

Conference | Proceedings of the 16th International Conference Algorithmic Learning Theory 2005 |
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Period | 31/12/05 → … |

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## Cite this

Chernov, A., & Hutter, M. (2005). Monotone conditional complexity bounds on future prediction errors. In

*Proceedings of the 16th International Conference Algorithmic Learning Theory 2005*(Vol. 3734, pp. 414-428). (Lecture Notes in Computer Science). Springer. https://doi.org/10.1007/11564089_32