Bad Universal Priors and Notions of Optimality

TL;DR

This paper investigates the dependence of the AIXI model's optimality on the choice of universal Turing machine, revealing that its performance and properties are highly subjective and can vary drastically with different UTMs.

Contribution

It demonstrates that AIXI's optimality and intelligence measures are not invariant and are heavily influenced by the choice of UTM, challenging previous assumptions.

Findings

AIXI's behavior can be drastically affected by the choice of UTM.

Legg-Hutter intelligence is subjective and varies with UTM.

All policies are Pareto optimal in the class of all computable environments.

Abstract

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.