Polynomial error bounds for computable patterns

Establish whether the exponential dependence on the program length in the upper bounds for Solomonoff-induction errors on computable patterns can be replaced by a polynomial dependence.

Background

Theorem 1 gives exponential upper bounds in the description length $k$ of a computable pattern for sums of powered prediction errors, as well as a corresponding finite-horizon bound. The authors explicitly identify the dependence on $k$ as a limitation of their result and leave open whether substantially sharper polynomial bounds are possible.