Couldn’t you just treat any ‘stochastic’ environment as hidden-variable theories—actually being a deterministic program with a PRNG appended whose seed you don’t know?
Yes, this is basically what I’m saying—treating the future as random, versus treating the future as encrypted by a one-time pad you don’t know, lead to the same distributions and behavior.
This means that if you want to think of Solomonoff induction in terms of random variables, you can, but it turns out that you get back something that’s still equivalent to Solomonoff induction.
Couldn’t you just treat any ‘stochastic’ environment as hidden-variable theories—actually being a deterministic program with a PRNG appended whose seed you don’t know?
Yes, this is basically what I’m saying—treating the future as random, versus treating the future as encrypted by a one-time pad you don’t know, lead to the same distributions and behavior.
This means that if you want to think of Solomonoff induction in terms of random variables, you can, but it turns out that you get back something that’s still equivalent to Solomonoff induction.
Yeah that seems right. But I’m not aware of any such work OTTMH.