That leaves a gap between cases in which the thief has access to the predictor/planner/reporter (which run into the diagonalization barrier), and cases in which the thief doesn’t even have detailed information about the diamond (in which case we can solve the problem). In between those, the thief has arbitrarily good information about the diamond, but does not have access to the predictor/planner/reporter.
For this case, I do not have a solution, but I do expect that it’s solvable-in-principle.
The main difficulty in these cases is that the P[Obs|do(A∗)] may be exactly the same between action-plans A∗ which result in the diamond being stolen, and action plans which do not. The thief has enough information to make the predicted sensor readings completely identical between the two cases.
The reason the problem might still be solvable-in-principle is that the actions A∗ still give us information about whether the diamond was stolen. But we somehow have to extract that information in a way which does not require any difference whatsoever between the observation-distributions in the two cases.
I was chewing over the ELK problem this morning and had a silly idea here. What if you deliberately introduce a specific inaccuracy in the camera, or the reporter? Have some timestamp or watermark or scratch, something that has to do with the system’s perception of the diamond and which would not be known from mere access to the diamond or at least be very expensive to fake.
I was chewing over the ELK problem this morning and had a silly idea here. What if you deliberately introduce a specific inaccuracy in the camera, or the reporter? Have some timestamp or watermark or scratch, something that has to do with the system’s perception of the diamond and which would not be known from mere access to the diamond or at least be very expensive to fake.