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I’m always surprised that more research doesn’t start from the mathematical “end” and work backwards to something that approximates it. For instance, assuming

I’m always surprised that more research doesn’t start from the mathematical “end” and work backwards to something that approximates it. For instance, assuming our universe is computable (or at least can be approximated to a high degree as computable), we know that Solomonoff induction is in some sense a mathematical upper bound on the best we could do at predicting the future. If we had a magical program that, given a sequence of data S, found the shortest (prefix free, non-halting) program that produced S, we would essentially have real AI (and the “best” AI, in some mathematical sense on general optimality over other algorithms). We know this is uncomputable, but I’m surprised that this fact seems to totally throw a wrench into at least approximating it. I suppose some efforts in reinforcement learning could sort of be considered attempts at this, but not really in the sense of mathematically developing the best physical implementation to solving the problem.

chriswarbo 5y ago
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)

chriswarbo 5y ago

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)