Chapter

Algorithmic Learning Theory

Volume 3734 of the series Lecture Notes in Computer Science pp 414-428

Monotone Conditional Complexity Bounds on Future Prediction Errors

  • Alexey ChernovAffiliated withCarnegie Mellon UniversityIDSIA
  • , Marcus HutterAffiliated withCarnegie Mellon UniversityIDSIA

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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 μ by the algorithmic complexity of μ. Here we assume we are at a time t>1 and already observed x=x 1...x t . We bound the future prediction performance on x t + 1 x t + 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.