Oh yes, that's one of the more recent papers from Hutter's group!
I don't believe there is a contradiction. AIXI is not computable and optimality is undecidable, this is true. "Asymptotic optimality" refers to behaviour for infinite time horizons. It does not refer to closeness to an optimal agent on a fixed time horizon. Naturally the claim that I made will break down in the infinite regime because the approximation rates do not scale with time well enough to guarantee closeness for all time under any suitable metric. Personally, I'm not interested in infinite time horizons and do not think it is an important criterion for "superintelligence" (we don't live in an infinite time horizon world after all) but that's a matter of philosophy, so feel free to disagree. I was admittedly sloppy with not explicitly stating that time horizons are considered finite, but that just comes from the choice of metric in the universal approximation which I have continued to be vague about. That also covers the Corollary 3.4, which is technically infinite time horizon (if I'm not mistaken) since the length of the string can be arbitrary.
I don't believe there is a contradiction. AIXI is not computable and optimality is undecidable, this is true. "Asymptotic optimality" refers to behaviour for infinite time horizons. It does not refer to closeness to an optimal agent on a fixed time horizon. Naturally the claim that I made will break down in the infinite regime because the approximation rates do not scale with time well enough to guarantee closeness for all time under any suitable metric. Personally, I'm not interested in infinite time horizons and do not think it is an important criterion for "superintelligence" (we don't live in an infinite time horizon world after all) but that's a matter of philosophy, so feel free to disagree. I was admittedly sloppy with not explicitly stating that time horizons are considered finite, but that just comes from the choice of metric in the universal approximation which I have continued to be vague about. That also covers the Corollary 3.4, which is technically infinite time horizon (if I'm not mistaken) since the length of the string can be arbitrary.