A notorious obstacle towards a solution of the problem of induction lies in the fact that the success object-inductive prediction methods (i.e. methods applied at the level of events) cannot be shown to be universally optimal. My proposal towards a solution of the problem of induction is meta-induction. By means of mathematical analysis and computer simulations of prediction games, I show that there exist meta-inductive prediction strategies whose success is universally optimal, modulo short-run losses which are upper-bounded. I explain the implications of my approach for the evolution of cognition, and suggest a revision of the paradigm of bounded rationality by introducing the distinction between local, general and universal prediction strategies.