# Solomonoff vs Bayes

From: Francois-Rene Rideau (fare@tunes.org)
Date: Sun May 13 2001 - 07:07:46 MDT

Are the people here speaking about the Bayesian approach to rationality
familiar with Solomonoff's principle of induction?
It seems to me that Solomonoff uncovers a bigger part of the picture
than just the Bayesian deduction principle.

Ray Solomonoff, one of the co-founders of the field of Algorithmic
Information Theory, simultaneously with Kolmogorov and Chaitin,
introduced a nice way to explain how rational induction is possible.
Roughly said, rational induction consists in dynamically trying to
find a minimal algorithmic model for the observations of the world;
when you add new observations, you try to find the minimal model update.
The actual probability measure is not computable, but can be computably
approximated from below. It verifies Bayes' theorem with respect to adding
new information. It depends on an algorithmic context, although up to a
constant factor, that tends toward one when comparing the outcome of two
different rational predictors faced with the same long sequences of random
observations. It thus defeats Karl Popper's limitation against
context-independent induction, by being context-dependent; yet with an
asymptotically irrelevant initial context. It is an induction principle
that neatly formalizes Moore's Law (commonly retro-stated as "pick the
simplest available explanation"). Now of course, see how a Solomonoff
predictor can only be _approximated_ by computational agents. This entails
that we (rational sentient beings, including AIs and ETs) are all irrational,
when faced with complex enough problems. However, there are convergent
algorithms to extract all information there is from "simple enough" systems
that can be described in rules polylogarithmically simpler than the observed
system. Etc.

Considering that, I'd rather say of rational agents that they are
Solomonovian than Bayesian.

PS: Solomonoff Induction is well-explained in chapter 5 of Li and Vitányi's
"Introduction to Kolmogorov Complexity and its Applications, 2nd Edition".

[ François-René ÐVB Rideau | Reflection&Cybernethics | http://fare.tunes.org ]
[ TUNES project for a Free Reflective Computing System | http://tunes.org ]
If the human mind were simple enough to understand,
we'd be too simple to understand it.
-- Pat Bahn

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