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Abstract
After generalizing the Archimedean property of real numbers in such a way as to make it adaptable to non-numeric structures, we demonstrate that the real numbers cannot be used to accurately measure non-Archimedean structures. We argue that, since an agent with Artificial General Intelligence (AGI) should have no problem engaging in tasks that inherently involve non-Archimedean rewards, and since traditional reinforcement learning rewards are real numbers, therefore traditional reinforcement learning cannot lead to AGI. We indicate two possible ways traditional reinforcement learning could be altered to remove this roadblock.
Keywords AGI  reinforcement learning  Archimedean property  nonstandard analysis
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Infinitesimal Gunk.Lu Chen - forthcoming - Journal of Philosophical Logic:1-24.
Non-Archimedean Probability.Vieri Benci, Leon Horsten & Sylvia Wenmackers - 2013 - Milan Journal of Mathematics 81 (1):121-151.
Non-Standard Analysis.A. Robinson - 1961 - North-Holland Publishing Co..

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