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skepsci comments on The mathematics of reduced impact: help needed - Less Wrong
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I don't understand much of this, and I want to, so let me start by asking basic questions in a much simpler setting.
We are playing Conway's game of life with some given initial state. An disciple AI is given a 5 by 5 region of the board and allowed to manipulate its entries arbitrarily - information leaves that region according to the usual rules for the game.
The master AI decides on some algorithm for the disciple AI to execute. Then it runs the simulation with and without the disciple AI. The results can be compared directly - by, for example, counting the number of squares where the two futures differ. This can be a measure of the "impact" of the AI.
What complexities am I missing? Is it mainly that Conway's game of life is deterministic and we are designing an AI for a stochastic world?
Exactly. If you have determinism in the sense of a function from AI action to result world, you can directly compute some measure of the difference between worlds X and X', where X is the result of AI inaction, and X' is the result of some candidate AI action.
As nerzhin points out, you can run into similar problems even in deterministic universes, including life, if the AI doesn't have perfect knowledge about the initial configuration or laws of the universe, or if the AI cares about differences between configurations that are so far into the future they are beyond the AI's ability to calculate. In this case, the universe might be deterministic, but the AI must reason in probabilities.