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2011

(Non-)Equivalence of Universal Priors

Wood, Ian, Sunehag, Peter, Hutter, Marcus

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Understand

Ray Solomonoff invented the notion of universal induction featuring an aptly termed "universal" prior probability function over all possible computable environments.

The essential property of this prior was its ability to dominate all other such priors.
Later, Levin introduced another construction --- a mixture of all possible priors or `universal mixture'.
These priors are well known to be equivalent up to multiplicative constants.

(Non-)Equivalence of Universal Priors · Around

Built on

On computable numbers, with an application to the Entscheidungsproblem
A. M. Turing · 1936
Earlier work this paper cites.
A formal theory of inductive inference: Parts 1 and 2
R. J. Solomonoff · 1964
Earlier work this paper cites.
The complexity of finite objects and the development of the concepts of information and randomness by means of the theory of algorithms
Original
A. K. Zvonkin and L. A. Levin · 1970
Earlier work this paper cites.
Some Theorems on the Algorithmic Approach to Probability Theory and Information Theory
Leonid A Levin · 1971
Earlier work this paper cites.

Similar

Process complexity and effective random tests
C. P. Schnorr · 1973
Cited alongside, same era.
A theory of program size formally identical to information theory
G. J. Chaitin · 1975
Cited alongside, same era.
Complexity-based induction systems: Comparisons and convergence theorems
R. J. Solomonoff · 1978
Cited alongside, same era.
Universal Artificial Intelligence: Sequential Decisions based on Algorithmic Probability
M. Hutter · 2005
Cited alongside, same era.

Then

Randomness and universal machines
S. Figueira, F. Stephan, and G. Wu · 2006
Later among the works it cites.
On universal prediction and Bayesian confirmation
M. Hutter · 2007
Later among the works it cites.
An Introduction to Kolmogorov Complexity and its Applications
M. Li and P. M. B. Vitányi · 2008
Later among the works it cites.
Algorithmic Randomness and Complexity
R. Downey and D. R. Hirschfeldt · 2010
Later among the works it cites.

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