Hume’s problem is the problem of establishing a justification of induction: the transfer of observed regularities from the past to the future. In this talk a new approach to Hume's problem is presented. The approach concedes the force of Hume’s sceptical arguments against the possibility of a non-circular justification of the reliability of induction. What it demonstrates is that one can nevertheless give a non-circular justification of the optimality of induction, more precisely of meta-induction, that is, induction applied at the level of competing methods of prediction. Based on discoveries in machine learning theory it is demonstrated that a strategy called attractivity-weighted meta-induction is predictively optimal in all possible worlds among all predic­tion methods accessible to the epistemic agent. The a priori justification of meta-induction generates a non-circular a posteriori justification of object-induction.