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.
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.