Intelligence via ultrafilters: structural properties of some intelligence comparators of deterministic Legg-Hutter agents

TL;DR

This paper introduces a novel method for comparing the relative intelligence of Legg-Hutter agents by modeling environments as voters in an election, leading to new structural insights into intelligence comparators.

Contribution

It proposes an innovative voting-based framework for comparing agent intelligence and proves structural theorems about these comparators, expanding theoretical understanding.

Findings

Structural theorems about intelligence comparators

Framework for comparing agents via environment votes

Open question on applicability to practical measures

Abstract

Legg and Hutter, as well as subsequent authors, considered intelligent agents through the lens of interaction with reward-giving environments, attempting to assign numeric intelligence measures to such agents, with the guiding principle that a more intelligent agent should gain higher rewards from environments in some aggregate sense. In this paper, we consider a related question: rather than measure numeric intelligence of one Legg- Hutter agent, how can we compare the relative intelligence of two Legg-Hutter agents? We propose an elegant answer based on the following insight: we can view Legg-Hutter agents as candidates in an election, whose voters are environments, letting each environment vote (via its rewards) which agent (if either) is more intelligent. This leads to an abstract family of comparators simple enough that we can prove some structural theorems about them. It is an open question whether these structural theorems apply to more practical intelligence measures.