Bad Universal Priors and Notions of Optimality
This is a foundational critique for researchers in algorithmic information theory and AI, revealing that AIXI's optimality is subjective and not invariant, which is incremental as it builds on prior work but challenges core assumptions.
The paper tackles the problem of the universal Turing machine (UTM) choice in algorithmic information theory, showing that for the AIXI agent, unlucky or adversarial UTM choices cause drastic misbehavior, undermining all existing optimality properties and making AIXI a relative theory dependent on UTM choice.
A 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.