ABSTRACT
The objective of Chapter 3 is to formally define the concept of a machine learning algorithm that makes rational inferences. The chapter begins with a discussion regarding how to formally model both discrete-time and continuous-time learning environments for machine learning algorithms. Next, dynamical systems concepts such as iterated maps and vector fields are used to model the dynamical behavior of a large class of machine learning algorithms. This large class of machine learning algorithms includes, as a special case, Turing machines which are models of classical digital computation. The computational goal of a machine learning algorithm is formally defined as making rational decisions with respect to a rational preference relation. Objective function minimization is then interpreted as making rational decisions with respect to a rational preference relation implicitly specified by the objective function. Finally, a linkage between the dynamical system representation of a machine learning algorithm and rational decision making is constructed by defining machine learning algorithms as dynamical systems that minimize an objective function. This linkage shows how machine learning algorithms may be viewed as machines that attempt to make rational decisions based upon a preference relation structure.
