Space and time are not really the right parameters here, since these refer to Φ (physical states), not Γ (computational “states”) or 2Γ (physically manifest facts about computations). In the example above, it doesn’t matter where the (copy of the) agent is when it sees the red room, only the fact the agent does see it. We could construct such a loss function by a sum over programs, but the constructions suggested in section 3 use minimum instead of sum, since this seems like a less “extreme” choice in some sense. Ofc ultimately the loss function is subjective: as long as the monotonicity principle is obeyed, the agent is free to have any loss function.
Space and time are not really the right parameters here, since these refer to Φ (physical states), not Γ (computational “states”) or 2Γ (physically manifest facts about computations). In the example above, it doesn’t matter where the (copy of the) agent is when it sees the red room, only the fact the agent does see it. We could construct such a loss function by a sum over programs, but the constructions suggested in section 3 use minimum instead of sum, since this seems like a less “extreme” choice in some sense. Ofc ultimately the loss function is subjective: as long as the monotonicity principle is obeyed, the agent is free to have any loss function.