One thing to keep in mind with all these "Universal AI" ideas (Hutter Search, Levin Search, Goedel Machines, etc.) is that they make very few assumptions about

One thing to keep in mind with all these "Universal AI" ideas (Hutter Search, Levin Search, Goedel Machines, etc.) is that they make very few assumptions about the task. That's their strength, but it's also what makes them hopelessly inefficient. We can get massive speedups by introducing a bit more structure, e.g. inverting differentiable functions rather than all functions makes it practical to use neural networks and their like; inverting convex functions lets us do simple hill climbing; etc. In the case of Hutter Search specifically, we could get much more promising results if we're willing to throw away Turing Completeness. For example, it's easier to find provable optimisations if we're dealing with regexps rather than arbitrary programs. Of course, such "easy" systems tend to have fast approaches already. I think there's definitely a role for these algorithms, but mostly as an "outer loop"; similar to using grid-search to find good hyperparameters of an ML model; or how we often throw genetic algorithms at tasks which have no 'obviously correct' solution (like choosing the architecture of a neural network)