I don't know to what extent MIRI's current research engages with Solomonoff induction, but some of you may find recent work by Tom Sterkenburg to be of interest. Here's the abstract of his paper Solomonoff Prediction and Occam's Razor:

Algorithmic information theory gives an idealised notion of compressibility that is often presented as an objective measure of simplicity. It is suggested at times that Solomonoff prediction, or algorithmic information theory in a predictive setting, can deliver an argument to justify Occam's razor. This article explicates the relevant argument and, by converting it into a Bayesian framework, reveals why it has no such justificatory force. The supposed simplicity concept is better perceived as a specific inductive assumption, the assumption of effectiveness. It is this assumption that is the characterising element of Solomonoff prediction and wherein its philosophical interest lies.

I don't think it's fair to say that "nobody understood induction in any kind of rigorous way until about 1968." The linked paper argues that Solomonoff prediction does not justify Occam's razor, but rather that it gives us a specific inductive assumption. And such inductive assumptions had previously been rigorously studied by Carnap among others.

But even if we grant that assumption, I don't see why we should find it surprising that science made progress without having a rigorous understanding of induction. In general, successfully engaging in so... (read more)