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| Bad Universal Priors and Notions of Optimality (2015) (arxiv.org) | |
| 1 point by chriswarbo on Jun 25, 2021 | hide | past | pdf | 1 comment on HN | |
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In plain words: AIXI, an ideal math model of a rational agent, guesses the world using a chosen universal computer, and unlike complexity measures its results can shift wildly with that choice. With a bad choice it misbehaves, and every strategy becomes equally "optimal" among computable worlds. Abstract · Bad Universal Priors and Notions of OptimalityA big open question of algorithmic information theory is the choice of the universal Turing machine (UTM). For Kolmogorov complexity and Solomonoff induction we have invariance theorems: the choice of the UTM changes bounds only by a constant. For the universally intelligent agent AIXI (Hutter, 2005) no invariance theorem is known. Our results are entirely negative: we discuss cases in which unlucky or adversarial choices of the UTM cause AIXI to misbehave drastically. We show that Legg-Hutter intelligence and thus balanced Pareto optimality is entirely subjective, and that every policy is Pareto optimal in the class of all computable environments. This undermines all existing optimality properties for AIXI. While it may still serve as a gold standard for AI, our results imply that AIXI is a relative theory, dependent on the choice of the UTM. | |
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This paper shows that the definition of AIXI and what is "optimal" are 'subjective': they depend heavily on which language(/turing machine) we decide to use. We can choose a language/TM which (a) causes AIXI to perform arbitrarily badly (worse than random); and (b) we can make "optimality" so trivial that it applies to every algorithm.