The simulation uses the input to determine the part of the initial conditions that specifies simulated-AIXI’s output voltages… ah! ah! ah! Found the Cartesian boundary! No matter how faithful the physics simulation is, AIXI only ever asks for one time-step at a time, so although the simulation’ state propagates to simulated-AIXI’s input voltages, it doesn’t propagate all the way through to the output voltage.
Actually, I find myself in a state of uncertainty as a result of doing a close reading section 2.6 of the Gentle Introduction to AIXI in light of your comment here. You quoted Paul Christiano as saying
Recall the definition of AIXI: A will try to infer a simple program which takes A’s outputs as input and provides A’s inputs as output, and then choose utility maximizing actions with respect to that program.
EY, Nate, Rob, and various commenters here (including myself until recently) all seemed to take this as given. For instance, above I wrote:
The simulation uses the input [i.e., action choice fed in as required by expectimax] to determine the part of the initial conditions that specifies simulated-AIXI’s output voltages [emphasis added]
On this “program-that-takes-action-choice-as-an-input” view (perhaps inspired by a picture like that on page 7 of the Gentle Introduction and surrounding text), a simulated event like, say, a laser cutter slicing AIXI’s (sim-)physical instantiation in half, could sever the (sim-)causal connection from (sim-)AIXI’s input wire to its output wire, and this event would not change the fact that the simulation specifies the voltage on the output wire from the expectimax action choice.
Your claim, if I understand you correctly, is that the AIXI formalism does not actually express this kind of back-and-forth state swapping. Rather, for any given universe-modeling program, it simulates forward from the specification of the (sim-)input wire voltage (or does something computationally equivalent), not from a specification of the (sim-)output wire voltage. There is some universe-model which simulates a computable approximation of all of (sim-)AIXI’s physical state changes; once the end state of has been specified, real-AIXI gives zero weight all branches of the expectimax tree that do not have an action that matches the state of (sim-)AIXI’s output wire.
Can you please expand?
Actually, I find myself in a state of uncertainty as a result of doing a close reading section 2.6 of the Gentle Introduction to AIXI in light of your comment here. You quoted Paul Christiano as saying
EY, Nate, Rob, and various commenters here (including myself until recently) all seemed to take this as given. For instance, above I wrote:
On this “program-that-takes-action-choice-as-an-input” view (perhaps inspired by a picture like that on page 7 of the Gentle Introduction and surrounding text), a simulated event like, say, a laser cutter slicing AIXI’s (sim-)physical instantiation in half, could sever the (sim-)causal connection from (sim-)AIXI’s input wire to its output wire, and this event would not change the fact that the simulation specifies the voltage on the output wire from the expectimax action choice.
Your claim, if I understand you correctly, is that the AIXI formalism does not actually express this kind of back-and-forth state swapping. Rather, for any given universe-modeling program, it simulates forward from the specification of the (sim-)input wire voltage (or does something computationally equivalent), not from a specification of the (sim-)output wire voltage. There is some universe-model which simulates a computable approximation of all of (sim-)AIXI’s physical state changes; once the end state of has been specified, real-AIXI gives zero weight all branches of the expectimax tree that do not have an action that matches the state of (sim-)AIXI’s output wire.
Do I have that about right?