With respect to the second question the answer will depend on the discount rate. I expect Solomonoff is assuming that we are in the limit of low discount rate, where exponential decay will look linear, so essentially you are minimizing the expected total number of attempts.
I haven’t done the math to confirm Somolonoff’s answer, but if you were to go to each box with probability equal to it being correct, then your expected number of attempts would be equal to the number of boxes, since each box would have an expected number of attempts conditional on it being the right box equal to the the inverse of its probability. So this is no better than choosing randomly. With this in mind it seems intuitive that some intermediate strategy, such as square roots, would then be better.
With respect to the second question the answer will depend on the discount rate. I expect Solomonoff is assuming that we are in the limit of low discount rate, where exponential decay will look linear, so essentially you are minimizing the expected total number of attempts.
I haven’t done the math to confirm Somolonoff’s answer, but if you were to go to each box with probability equal to it being correct, then your expected number of attempts would be equal to the number of boxes, since each box would have an expected number of attempts conditional on it being the right box equal to the the inverse of its probability. So this is no better than choosing randomly. With this in mind it seems intuitive that some intermediate strategy, such as square roots, would then be better.
https://www.reddit.com/r/compsci/comments/7yd765/reference_request_on_a_result_by_ray_solomonoff/