Abstract
Solomonoff induction and AIXI model their environment as an arbitrary Turing machine, but are themselves uncomputable. This fails to capture an essential property of real-world agents, which cannot be more powerful than the environment they are embedded in; for example, AIXI cannot accurately model game-theoretic scenarios in which its opponent is another instance of AIXI.
In this paper, we define reflective variants of Solomonoff induction and AIXI, which are able to reason about environments containing other, equally powerful reasoners. To do so, we replace Turing machines by probabilistic oracle machines (stochastic Turing machines with access to an oracle). We then use reflective oracles, which answer questions of the form, “is the probability that oracle machine \(T\) outputs 1 greater than p, when run on this same oracle?” Diagonalization can be avoided by allowing the oracle to answer randomly if this probability is equal to p; given this provision, reflective oracles can be shown to exist. We show that reflective Solomonoff induction and AIXI can themselves be implemented as oracle machines with access to a reflective oracle, making it possible for them to model environments that contain reasoners as powerful as themselves.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Fallenstein, B., Soares, N.: Vingean reflection: Reliable reasoning for self-modifying agents. Tech. Rep. 2015–2, Machine Intelligence Research Institute (2015). https://intelligence.org/files/VingeanReflection.pdf
Fallenstein, B., Taylor, J., Christiano, P.F.: Reflective oracles: A foundation for classical game theory. Tech. Rep. 2015–7, Machine Intelligence Research Institute (2015). https://intelligence.org/files/ReflectiveOracles.pdf
Hutter, M.: Universal algorithmic intelligence. In: Goertzel, B., Pennachin, C. (eds.) Artificial General Intelligence, pp. 227–290. Springer, Cognitive Technologies (2007)
Hutter, M.: Open problems in universal induction & intelligence. Algorithms 2(3), 879–906 (2009)
Legg, S., Hutter, M.: Universal intelligence. Minds and Machines 17(4), 391–444 (2007)
Orseau, L., Ring, M.: Space-Time Embedded Intelligence. In: Bach, J., Goertzel, B., Iklé, M. (eds.) AGI 2012. LNCS, vol. 7716, pp. 209–218. Springer, Heidelberg (2012)
Soares, N.: Formalizing two problems of realistic world-models. Tech. Rep. 2015–3, Machine Intelligence Research Institute (2015). https://intelligence.org/files/RealisticWorldModels.pdf
Solomonoff, R.J.: A formal theory of inductive inference. Part I. Information and Control 7(1), 1–22 (1964)
Vallinder, A.: Solomonoff Induction: A Solution to the Problem of the Priors? MA thesis, Lund University (2012). http://lup.lub.lu.se/luur/download?func=downloadFile&recordOId=3577211&fileOId=3577215
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Fallenstein, B., Soares, N., Taylor, J. (2015). Reflective Variants of Solomonoff Induction and AIXI. In: Bieger, J., Goertzel, B., Potapov, A. (eds) Artificial General Intelligence. AGI 2015. Lecture Notes in Computer Science(), vol 9205. Springer, Cham. https://doi.org/10.1007/978-3-319-21365-1_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-21365-1_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-21364-4
Online ISBN: 978-3-319-21365-1
eBook Packages: Computer ScienceComputer Science (R0)