Reward-Punishment Symmetric Universal Intelligence

TL;DR

This paper extends the Legg-Hutter framework to include punishments, demonstrating that under certain symmetries, agents can have negative or zero intelligence levels, challenging traditional notions of intelligence measurement.

Contribution

It introduces a symmetry-based extension to the Legg-Hutter measure, allowing for negative and zero intelligence values under specific conditions.

Findings

Intelligence can be negative with punishment considerations.

Symmetry conditions lead to a zero intelligence baseline.

Reward-ignoring agents have zero Legg-Hutter intelligence.

Abstract

Can an agent's intelligence level be negative? We extend the Legg-Hutter agent-environment framework to include punishments and argue for an affirmative answer to that question. We show that if the background encodings and Universal Turing Machine (UTM) admit certain Kolmogorov complexity symmetries, then the resulting Legg-Hutter intelligence measure is symmetric about the origin. In particular, this implies reward-ignoring agents have Legg-Hutter intelligence 0 according to such UTMs.