the maximally unexpected sequence will be random
In a random sequence, AIXI would guess on average half of the bits. My goal was to create a specific sequence, where it couldn't guess any. Not just a random sequence, but specifically... uhm... "anti-inductive"? The exact opposite of lawful, where random is merely halfway opposed. I don't care about other possible predictors, only about AIXI.
Imagine playing rock-paper-scissors against someone who beats you all the time, whatever you do. That's worse than random. This sequence would bring the mighty AIXI to tears... but I suspect to a human observer it would merely seem pseudo-random. And is probably not very useful for other goals than making fun of AIXI.
Ok. I still think the sequence is random in the algorithmic information theory sense; i.e., it's incompressible. But I understand you're interested in the adversarial aspect of the scenario.
You only need a halting oracle to compute your adversarial sequence (because that's what it takes to run AIXI). A super-Solomonoff inductor that inducts over all Turing machines with access to halting oracles would be able to learn the sequence, I think. The adversarial sequence for that inductor would require a higher oracle to compute, and so on up the ordinal hierarchy.
Previous Open Thread
You know the drill - If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
Notes for future OT posters:
1. Please add the 'open_thread' tag.
2. Check if there is an active Open Thread before posting a new one.
3. Open Threads should start on Monday, and end on Sunday.
4. Open Threads should be posted in Discussion, and not Main.