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Axioms for Rational Reinforcement Learning

  • Peter Sunehag
  • Marcus Hutter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6925)

Abstract

We provide a formal, simple and intuitive theory of rational decision making including sequential decisions that affect the environment. The theory has a geometric flavor, which makes the arguments easy to visualize and understand. Our theory is for complete decision makers, which means that they have a complete set of preferences. Our main result shows that a complete rational decision maker implicitly has a probabilistic model of the environment. We have a countable version of this result that brings light on the issue of countable vs finite additivity by showing how it depends on the geometry of the space which we have preferences over. This is achieved through fruitfully connecting rationality with the Hahn-Banach Theorem. The theory presented here can be viewed as a formalization and extension of the betting odds approach to probability of Ramsey and De Finetti [Ram31, deF37].

Keywords

Rationality Probability Utility Banach Space Linear Functional 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Peter Sunehag
    • 1
  • Marcus Hutter
    • 1
  1. 1.Research School of Computer ScienceAustralian National UniversityCanberraAustralia

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