Not quite. If taking bet 9 is a prerequisite to taking bet 10, then AIXI won’t take bet 9, but if bet 10 gets offered whether or not bet 9 is accepted, then AIXI will be like “ah, future me will take the bet, and wind up with 10+ϵ in the heads world and −20+2ϵ in the tails world. This is just a given. I’ll take this +15/-15 bet as it has net positive expected value, and the loss in the heads world is more than counterbalanced by the reduction in the magnitude of loss for the tails world”
Something else feels slightly off, but I can’t quite pinpoint it at this point. Still, I guess this solves my question as originally stated, so I’ll PM you for payout. Well done!
(btw, you can highlight a string of text and hit crtl+4 to turn it into math-mode)
I figured out what feels slightly off about this solution. For events like “I have a long memory and accidentally dropped a magnet on it”, it intuitively feels like describing your spot in the environment and the rules of your environment is much lower K-complexity than finding a turing machine/environment that starts by giving you the exact (long) scrambled sequence of memories that you have, and then resumes normal operating.
Although this also feels like something nearby is actually desired behavior. If you rewrite the tape to be describing some other simple environment, you would intuitively expect the AIXI to act as if it’s in the simple environment for a brief time before gaining enough information to conclude that things have changed and rederive the new rules of where it is.
Well, it COULD be the case that the K-complexity of the memory-erased AIXI environment is lower, even when it learns that this happened. The reason for this is that there could be many possible past AIXI’s who have their memory erased/altered and end up in the same subjective situation. Then the memory-erasure hypothesis can use the lowest K-complexity AIXI who ends up with these memories. As the AIXI learns more it can gradually piece together which of the potential past AIXI’s it actually was and the K-complexity will go back up again.
EDIT: Oh, I see you were talking about actually having a RANDOM memory in the sense of a random sequence of 1s and 0s. Yeah, but this is no different than AIXI thinking that any random process is high K-complexity. In general, and discounting merging, the memory-altering subroutine will increase the complexity of the environment by a constant plus the complexity of whatever transformation you want to apply to the memories.
Not quite. If taking bet 9 is a prerequisite to taking bet 10, then AIXI won’t take bet 9, but if bet 10 gets offered whether or not bet 9 is accepted, then AIXI will be like “ah, future me will take the bet, and wind up with 10+ϵ in the heads world and −20+2ϵ in the tails world. This is just a given. I’ll take this +15/-15 bet as it has net positive expected value, and the loss in the heads world is more than counterbalanced by the reduction in the magnitude of loss for the tails world”
Something else feels slightly off, but I can’t quite pinpoint it at this point. Still, I guess this solves my question as originally stated, so I’ll PM you for payout. Well done!
(btw, you can highlight a string of text and hit crtl+4 to turn it into math-mode)
I figured out what feels slightly off about this solution. For events like “I have a long memory and accidentally dropped a magnet on it”, it intuitively feels like describing your spot in the environment and the rules of your environment is much lower K-complexity than finding a turing machine/environment that starts by giving you the exact (long) scrambled sequence of memories that you have, and then resumes normal operating.
Although this also feels like something nearby is actually desired behavior. If you rewrite the tape to be describing some other simple environment, you would intuitively expect the AIXI to act as if it’s in the simple environment for a brief time before gaining enough information to conclude that things have changed and rederive the new rules of where it is.
Well, it COULD be the case that the K-complexity of the memory-erased AIXI environment is lower, even when it learns that this happened. The reason for this is that there could be many possible past AIXI’s who have their memory erased/altered and end up in the same subjective situation. Then the memory-erasure hypothesis can use the lowest K-complexity AIXI who ends up with these memories. As the AIXI learns more it can gradually piece together which of the potential past AIXI’s it actually was and the K-complexity will go back up again.
EDIT: Oh, I see you were talking about actually having a RANDOM memory in the sense of a random sequence of 1s and 0s. Yeah, but this is no different than AIXI thinking that any random process is high K-complexity. In general, and discounting merging, the memory-altering subroutine will increase the complexity of the environment by a constant plus the complexity of whatever transformation you want to apply to the memories.