  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...x_t. We bound
the future prediction performance on x_{t+1}x_{t+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.
