Algorithmic complexity bounds on future prediction errors

Alexey Chernov, Marcus Hutter, Juergen Schmidhuber

Research output: Contribution to journalArticlepeer-review


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 μ by the algorithmic complexity of μ . Here we assume that we are at a time t>1 and have already observed x = x 1...xt . We bound the future prediction performance on xt+1xt+2... by a new variant of algorithmic complexity of μ 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 languageEnglish
Pages (from-to)242-261
Number of pages20
JournalInformation And Computation
Issue number2
Publication statusPublished - 28 Feb 2007

Bibliographical note

© 2007. This manuscript version is made available under the CC-BY-NC-ND 4.0 license


  • Kolmogorov complexity
  • posterior bounds
  • online sequential prediction
  • Solomonoff prior
  • monotone conditional complexity
  • total error
  • future loss
  • randomness deficiency


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