Explicit Legg-Hutter Intelligence Calculations Which Suggest Non-Archimedean Intelligence

Samuel Allen Alexander, Arthur Paul Pedersen

Abstract: Are the real numbers rich enough to measure intelligence? We generalize a result of Alexander and Hutter about the so-called Legg-Hutter intelligence measures of reinforcement learning agents. Using the generalized result, we exhibit a paradox: in one particular version of the Legg-Hutter intelligence measure, certain agents all have intelligence 0, even though in a certain sense some of them outperform others. We show that this paradox disappears if we vary the Legg-Hutter intelligence measure to be hyperreal-valued rather than real-valued.

External IDs:doi:10.1007/978-3-031-94748-3_13