Intervention Complexity as a Canonical Reward and a Measure of Intelligence
This work provides a principled solution to the arbitrariness of reward functions in universal intelligence measures, which is foundational for theoretical AI and agent evaluation.
The paper introduces intervention complexity as a canonical reward function for the Legg-Hutter universal intelligence measure, eliminating the need for externally specified rewards. It also proposes a two-dimensional characterization of intelligence (competence and learning efficiency) and shows that the computability of the measure depends on the resource bias.
The Legg--Hutter universal intelligence measure provides a rigorous scalar assessment of general intelligence as expected reward across all computable environments, weighted by simplicity. However, the measure presupposes an externally specified reward function, raising the question of whether the reward primitive is inherently arbitrary or whether a canonical choice exists. We propose a new measure, called intervention complexity, that has five natural properties: environment-derivedness, universality, minimality, sensitivity, and achievement preference. Given a resource function rho encoding an inductive bias (such as program length, execution time, or energy), rho-intervention complexity is a universal reward. The result yields a family of canonical rewards indexed by resource bias, providing a principled completion of the Legg--Hutter framework that does not require external normative input. We further propose a two-dimensional characterisation of intelligence: agent competence (how well the agent performs relative to the oracle optimum) and learning efficiency (how quickly this competence improves with experience). A separation theorem establishes that the choice of resource bias determines the computability of the resulting measure: action-count IC is computable in polynomial time, while program-length IC without oracle access is uncomputable, with the gap between oracle and bare IC precisely quantifying the information-theoretic content of learning. We discuss implications for superintelligence and for pre-training universal agents.