48 research outputs found
Principles of Solomonoff Induction and AIXI
We identify principles characterizing Solomonoff Induction by demands on an
agent's external behaviour. Key concepts are rationality, computability,
indifference and time consistency. Furthermore, we discuss extensions to the
full AI case to derive AIXI.Comment: 14 LaTeX page
A Philosophical Treatise of Universal Induction
Understanding inductive reasoning is a problem that has engaged mankind for
thousands of years. This problem is relevant to a wide range of fields and is
integral to the philosophy of science. It has been tackled by many great minds
ranging from philosophers to scientists to mathematicians, and more recently
computer scientists. In this article we argue the case for Solomonoff
Induction, a formal inductive framework which combines algorithmic information
theory with the Bayesian framework. Although it achieves excellent theoretical
results and is based on solid philosophical foundations, the requisite
technical knowledge necessary for understanding this framework has caused it to
remain largely unknown and unappreciated in the wider scientific community. The
main contribution of this article is to convey Solomonoff induction and its
related concepts in a generally accessible form with the aim of bridging this
current technical gap. In the process we examine the major historical
contributions that have led to the formulation of Solomonoff Induction as well
as criticisms of Solomonoff and induction in general. In particular we examine
how Solomonoff induction addresses many issues that have plagued other
inductive systems, such as the black ravens paradox and the confirmation
problem, and compare this approach with other recent approaches.Comment: 72 pages, 2 figures, 1 table, LaTe
Solomonoff Induction: A Solution to the Problem of the Priors?
In this essay, I investigate whether Solomonoff’s prior can be used to solve the problem of the priors for Bayesianism. In outline, the idea is to give higher prior probability to hypotheses that are "simpler", where simplicity is given a precise formal definition. I begin with a review of Bayesianism, including a survey of past proposed solutions of the problem of the priors. I then introduce the formal framework of Solomonoff induction, and go through some of its properties, before finally turning to some applications. After this, I discuss several potential problems for the framework. Among these are the fact that Solomonoff’s prior is incomputable, that the prior is highly dependent on the choice of a universal Turing machine to use in the definition, and the fact that it assumes that the hypotheses under consideration are computable. I also discuss whether a bias toward simplicity can be justified. I argue that there are two main considerations favoring Solomonoff’s prior: (i) it allows us to assign strictly positive probability to every hypothesis in a countably infinite set in a non-arbitrary way, and (ii) it minimizes the number of "retractions" and "errors" in the worst case