Solomonoff induction

TL;DR

This paper examines Solomonoff induction as a universal prediction method, highlighting its theoretical foundations, limitations due to computability issues, and its implications for principles like Occam's razor and machine learning.

Contribution

It critically analyzes Solomonoff induction, demonstrating its limitations and discussing its potential and challenges as a foundational framework for prediction and learning.

Findings

Solomonoff induction faces fundamental computability limitations.

The approach does not fully meet the desired computability criteria.

It offers insights into the theoretical basis of Occam's razor and machine learning.

Abstract

This chapter discusses the Solomonoff approach to universal prediction. The crucial ingredient in the approach is the notion of computability, and I present the main idea as an attempt to meet two plausible computability desiderata for a universal predictor. This attempt is unsuccessful, which is shown by a generalization of a diagonalization argument due to Putnam. I then critically discuss purported gains of the approach, in particular it providing a foundation for the methodological principle of Occam's razor, and it serving as a theoretical ideal for the development of machine learning methods.