Sequential Predictions based on Algorithmic Complexity

This paper studies sequence prediction based on the monotone Kolmogorov complexity Km= logm, i.e. based on universal deterministic/one-part MDL. m is extremely close to Solomono ’s universal priorM , the latter being an excellent predictor in deterministic as well as probabilistic environments, where performance is measured in terms of convergence of posteriors or losses. Despite this closeness to M , it is di cult to assess the prediction quality of m, since little is known about the closeness of their posteriors, which are the important quantities for prediction. We show that for deterministic computable environments, the \posterior" and losses ofm converge, but rapid convergence could only be shown on-sequence; the o -sequence convergence can be slow. In probabilistic environments, neither the posterior nor the losses converge, in general.