Hume's problem is located in the fact that no inductive prediction strategy can be universally reliable (i.e., reliable in all possible worlds). But there exists another kind of epistemic justification which is (loosely speaking) weaker than a justification-as-reliable, namely a justification-as-optimal (first suggested by Reichenbach). It is easy to show that there cannot exist an universally optimal object-inductive prediction strategy (i.e., one who applies induction at the level of events). In my talk I want to show, however, that so-called meta-inductive prediction strategies (who apply induction at the level of competing prediction strategies) can be universally optimal among all accessible prediction strategies. I will demonstrate by mathematical proof and computer simulations that there exist meta-inductive prediction strategies whose success is long-run optimal in all possible prediction games, and whose short-run loss is small. The proposed justification of meta-induction is mathematically analytical. It entails, however, an a posteriori justification of object-induction based on the experiences in our world.