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MrMind comments on Versions of AIXI can be arbitrarily stupid - Less Wrong Discussion

15 Post author: Stuart_Armstrong 10 August 2015 01:23PM

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Comment author: buybuydandavis 11 August 2015 07:48:02PM 5 points [-]

then an AIXI that follows one prior can be arbitrarily stupid with respect to another.

Yet another application of David Wolpert's No Free Lunch theorems.

We have dubbed the associated results NFL theorems because they demonstrate that if an algorithm performs well on a certain class of problems then it necessarily pays for that with degraded performance on the set of all remaining problems.

https://en.wikipedia.org/wiki/No_free_lunch_theorem

Comment author: MrMind 12 August 2015 10:09:58AM 1 point [-]

NFL works with algorithms operating on finite problems. With algorithms operating on unbounded problems, you can benefit from Blum's speedup theorem: for every algorithm and every computable measure of performance, there's a second algorithm performing better than the first on almost all inputs.

I suspect here's happening something similar: AIXI is finitely bias-able, and there are environments that can exploit that to arbitrarily constrain the agent's behaviour. If the analogy holds, there's then a class of environments for which AIXI, however finitely biased, is still optimally intelligent.