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The Archimedean trap: Why traditional reinforcement learning will probably not yield AGI Cover

The Archimedean trap: Why traditional reinforcement learning will probably not yield AGI

Open Access
|Oct 2020

References

  1. Al-Dhalimy, H., and Geyer, C. J. 2016. Surreal Time and Ultratasks. The Review of Symbolic Logic 9(4):836–847.10.1017/S1755020316000289
  2. Alexander, S. A. 2019a. Intelligence via ultrafilters: structural properties of some intelligence comparators of deterministic Legg-Hutter agents. Journal of Artificial General Intelligence 10:24–45.10.2478/jagi-2019-0003
  3. Alexander, S. A. 2019b. Measuring the intelligence of an idealized mechanical knowing agent. In Cognition, Interdisciplinary Foundations, Models, and Applications (CIFMA).10.1007/978-3-030-57506-9_13
  4. Andréka, H.; Madarász, J. X.; Németi, I.; and Székely, G. 2012. A logic road from special relativity to general relativity. Synthese 186(3):633–649.10.1007/s11229-011-9914-8
  5. Archimedes. 1897. On the Sphere and Cylinder. In Heath, T., ed., The works of Archimedes. Cambridge University Press.
  6. Bair, J.; B laszczyk, P.; Ely, R.; Henry, V.; Kanovei, V.; Katz, K. U.; Katz, M. G.; Kutateladze, S. S.; McGaffey, T.; Schaps, D. M.; Sherry, D.; and Shnider, S. 2013. Is mathematical history written by the victors? Notices of the American Mathematical Society 60(7):886–904.
  7. Benci, V.; Horsten, L.; and Wenmackers, S. 2013. Non-Archimedean probability. Milan Journal of Mathematics 81(1):121–151.10.1007/s00032-012-0191-x
  8. Blum, D., and Holling, H. 2017. Spearman’s law of diminishing returns. A meta-analysis. Intelligence 65:60–66.
  9. Chen, L. 2020. Infinitesimal gunk. Journal of Philosophical Logic 49:981–1004.10.1007/s10992-020-09544-x
  10. Conway, J. H. 2000. On Numbers and Games. CRC Press, 2nd edition.10.1201/9781439864159
  11. Ehrlich, P. 2012. The absolute arithmetic continuum and the unification of all numbers great and small. Bulletin of Symbolic Logic 18:1–45.10.2178/bsl/1327328438
  12. Euclid. 2007. Book V: Theory of Proportion. In Casey, J., ed., First Six Books of the Elements of Euclid. Project Gutenburg.
  13. Hernández-Orallo, J. 2019. AI Generality and Spearman’s Law of Diminishing Returns. Journal of Artificial Intelligence Research 64:529–562.10.1613/jair.1.11388
  14. Hibbard, B. 2011. Measuring agent intelligence via hierarchies of environments. In International Conference on Artificial General Intelligence, 303–308. Springer.10.1007/978-3-642-22887-2_34
  15. Knuth, D. E. 1974. Surreal numbers: a mathematical novelette. Addison-Wesley.
  16. Legg, S., and Hutter, M. 2007. Universal intelligence: A definition of machine intelligence. Minds and machines 17(4):391–444.10.1007/s11023-007-9079-x
  17. Livingston, S.; Garvey, J.; and Elhanany, I. 2008. On the broad implications of reinforcement learning based AGI. In International Conference on Artificial General Intelligence, 478–482.
  18. Maruyama, Y. 2020. Symbolic and Statistical Theories of Cognition: Towards Integrated Artificial Intelligence. In Cognition, Interdisciplinary Foundations, Models, and Applications (CIFMA).
  19. Mill, J. S. 2016. Utilitarianism. In Seven masterpieces of philosophy. Routledge. 337–383.10.4324/9781315508818-12
  20. Narens, L. 1974. Measurement without Archimedean axioms. Philosophy of Science 41(4):374–393.10.1086/288600
  21. Niederée, R. 1992. What do numbers measure?: A new approach to fundamental measurement. Mathematical Social Sciences 24(2-3):237–276.10.1016/0165-4896(92)90063-B
  22. Plato. 1997. Protagoras. In Cooper, J. M.; Hutchinson, D. S.; et al., eds., Plato: complete works. Hackett Publishing.
  23. Pohlers, W. 2008. Proof theory: The first step into impredicativity. Springer.
  24. Rathjen, M. 2006. The art of ordinal analysis. In Proceedings of the International Congress of Mathematicians, volume 2, 45–69.
  25. Reeder, P. F. 2012. Infinitesimals for Metaphysics: Consequences for the Ontologies of Space and Time. Ph.D. Dissertation, The Ohio State University.
  26. Rizza, D. 2016. Divergent Mathematical Treatments in Utility Theory. Erkenntnis 81(6):1287–1303.10.1007/s10670-015-9795-1
  27. Robinson, A. 1974. Non-standard analysis. Princeton University Press.
  28. Rosinger, E. E. 2007. Cosmic Contact: To Be, or Not To Be Archimedean? arXiv preprint physics/0702206.
  29. Skala, H. J. 1975. Non-Archimedean utility theory. D. Reidel Publishing.10.1007/978-94-010-1724-4
  30. Spearman, C. 1927. The abilities of man. Macmillan.
  31. Tall, D. 1980. Looking at graphs through infinitesimal microscopes, windows and telescopes. The Mathematical Gazette 64:22–49.10.2307/3615886
  32. Veldhuizen, T. L. 2003. C++ Templates are Turing Complete. Technical report, Indiana University.
  33. Wang, P., and Hammer, P. 2015. Assumptions of decision-making models in AGI. In International Conference on Artificial General Intelligence, 197–207. Springer.10.1007/978-3-319-21365-1_21
  34. Wirth, C.; Akrour, R.; Neumann, G.; and Fürnkranz, J. 2017. A survey of preference-based reinforcement learning methods. The Journal of Machine Learning Research 18(1):4945–4990.
  35. Zhao, Y.; Kosorok, M. R.; and Zeng, D. 2009. Reinforcement learning design for cancer clinical trials. Statistics in medicine 28(26):3294–3315.10.1002/sim.3720276741819750510
Language: English
Page range: 70 - 85
Submitted on: Feb 16, 2020
Accepted on: Sep 29, 2020
Published on: Oct 15, 2020
Published by: Artificial General Intelligence Society
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2020 Samuel Allen Alexander, published by Artificial General Intelligence Society
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.