Axioms for Rational Reinforcement Learning

TL;DR

This paper develops a geometric, axiomatic framework for rational decision making in sequential environments, showing that complete rational agents implicitly possess probabilistic models, and connecting rationality with the Hahn-Banach Theorem.

Contribution

It introduces a formal, intuitive theory of rational decision making that links preferences to probabilistic models using geometric and functional analysis tools.

Findings

Complete rational decision makers have implicit probabilistic models.

The geometric approach clarifies the role of countable vs finite additivity.

The theory extends the betting odds approach of Ramsey and De Finetti.

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.