Thx for the references! I was familiar with Hernandez-Orallo et al. (2011) and Goertzel (2010).
However, it seems that none of these papers tackles the Duality problem.
Regarding environmental distributions, I think this problem is solved rather elegantly in my approach by the quasi-Solomonoff distribution, which singles out environments compatible with the tentative model D. Essentially it is the Solomonoff prior updated by a period of observations during which D-behavior was seen.
Regarding the choice of a reference machine, its role asymptotically vanishes in the tail of the Solomonoff distribution. The quasi-Solomonoff distribution samples the tail of the Solomonoff distribution by design, the more so the more complex is D.
In applications it seems to be a good idea to use D as complex as possible (i.e. put in as much as possible information about the universe) while using a reference machine as simple as possible. In fact I would use lambda-calculus rather than a Turing machine. This is because the simpler the reference machine the closer the relation between the Solomonoff distirbution and Occam’s razor. If we assume that our intuitive grasp of simplicity is approximately correct then using a complex reference machine doesn’t make sense.
Thx for the references! I was familiar with Hernandez-Orallo et al. (2011) and Goertzel (2010).
However, it seems that none of these papers tackles the Duality problem.
Regarding environmental distributions, I think this problem is solved rather elegantly in my approach by the quasi-Solomonoff distribution, which singles out environments compatible with the tentative model D. Essentially it is the Solomonoff prior updated by a period of observations during which D-behavior was seen.
Regarding the choice of a reference machine, its role asymptotically vanishes in the tail of the Solomonoff distribution. The quasi-Solomonoff distribution samples the tail of the Solomonoff distribution by design, the more so the more complex is D.
In applications it seems to be a good idea to use D as complex as possible (i.e. put in as much as possible information about the universe) while using a reference machine as simple as possible. In fact I would use lambda-calculus rather than a Turing machine. This is because the simpler the reference machine the closer the relation between the Solomonoff distirbution and Occam’s razor. If we assume that our intuitive grasp of simplicity is approximately correct then using a complex reference machine doesn’t make sense.