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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.

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

  • 会议论文

  • 发表日期：

    2026年

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  • Samuel Allen Alexander,
  • Arthur Paul Pedersen

摘要

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.