Aren’t the universe weights just probabilities by a different name? (Which leads directly to my formulation “UDT = choose the strategy that maximizes your unconditional expected utility”.) Or are the weights supposed to be subjective—they measure the degree to which you ‘care’ about the various worlds, and different agents can assign different weights without either one being ‘wrong’? But doesn’t that contradict that idea that we’re supposed to use the One True Solomonoff Prior?
Or are you not thinking of the weights as probabilities simply because UDT does away with the idea that one of the possible worlds is ‘true’ and all the others are ‘false’?
If the weights are probabilities, then what are they probabilities of? On some level, the notion of a computation “being” in one specific universe is incoherent. A sorting algorithm that is invoked to sort the array (1,3,2) finds itself simultaneously “in” all the universes that run it. From the computation’s point of view, there really is no fact of the matter as to “where” it is. Grasping this idea while thinking of your own thought process as a computation can really blow a person’s mind :-)
UDT doesn’t require the Solomonoff prior, it’s fine with whatever prior you choose. We already know that the Solomonoff prior can’t be the final solution, because it depends on the choice of programming langage (or universal machine). Me, I don’t like these huge priors. Applying UDT to little toy problems is mathematically interesting enough for me.
Aren’t the universe weights just probabilities by a different name? (Which leads directly to my formulation “UDT = choose the strategy that maximizes your unconditional expected utility”.) Or are the weights supposed to be subjective—they measure the degree to which you ‘care’ about the various worlds, and different agents can assign different weights without either one being ‘wrong’? But doesn’t that contradict that idea that we’re supposed to use the One True Solomonoff Prior?
Or are you not thinking of the weights as probabilities simply because UDT does away with the idea that one of the possible worlds is ‘true’ and all the others are ‘false’?
If the weights are probabilities, then what are they probabilities of? On some level, the notion of a computation “being” in one specific universe is incoherent. A sorting algorithm that is invoked to sort the array (1,3,2) finds itself simultaneously “in” all the universes that run it. From the computation’s point of view, there really is no fact of the matter as to “where” it is. Grasping this idea while thinking of your own thought process as a computation can really blow a person’s mind :-)
UDT doesn’t require the Solomonoff prior, it’s fine with whatever prior you choose. We already know that the Solomonoff prior can’t be the final solution, because it depends on the choice of programming langage (or universal machine). Me, I don’t like these huge priors. Applying UDT to little toy problems is mathematically interesting enough for me.