The Archimedean trap: Why traditional reinforcement learning will probably not yield AGI
This work identifies a theoretical limitation in RL for AGI, which is significant for AI researchers but incremental as it builds on mathematical generalizations without empirical validation.
The paper argues that traditional reinforcement learning (RL) likely cannot achieve Artificial General Intelligence (AGI) because RL uses real numbers for rewards, which cannot accurately measure non-Archimedean structures inherent in AGI tasks, and suggests two potential modifications to address this limitation.
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 probably will not lead to AGI. We indicate two possible ways traditional reinforcement learning could be altered to remove this roadblock.