Ask and ye shall be answered

by Stuart_Armstrong1 min read18th Sep 20153 comments

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A putative new idea for AI control; index here.

EDIT: the mathematics of this idea can be found here.

It would be useful to have a mechanism for getting an AI to provide an honest answer to a specific question. This post presents such a mechanism.

The question is: what is the impact of X/¬X on the expected utility of a utility function v? Here X/¬X is some well-defined binary outcome. Formally, for a constant c (positive or negative), we want to query the AI as to whether Q(v,X,c) is true, where

Q(v,X,c) = {E(v|X) - E(v|¬X) > c}.

How can we do that? Well, for a start, let M(u) be a u-maximising agent. We'll assume we can feed M() any utility function to maximise. We'll further assume that M() is boxed, that it has a single output bit Y (or ¬Y), and that we have cut any acausal trade possibilities. We'll add another binary process Z, which, if Z=1, erases the bit from Y before we can see it. In actual fact, P(Z=0)≈1.

The remaining assumptions are on the operations we can perform on v (without needing any further understanding of v). We replace v by v#, defined in the following way. First of all, we make v# indifferent to worlds in which X≠Y or Z=0 (note: there are subtleties to defining indifference to events that are partially under the AI's control; I will address these in a later post). Therefore any v# maximiser will behave as if it lived in a world where X=Y (its output and the outcome of X were the same) and Z=1 (its output was erased and never read). Then we add a special, one-off penalty of -c for outputting Y=1 (there is no effect for outputting Y=0). This defines v#, and we give our boxed AI v# to maximise.

So, how will M(v#) behave? Because it acts as if X=Y with certainty, it behaves as if it can determine the value of X by outputting Y. Because it acts as if Z=0 with certainty, it behaves as if the output of Y is never read, so it can determine the value of X without affecting anything else about the universe. It will now behave as if it was a v maximiser with control over X. So if it outputs ¬Y, it expects to get utility E(v|¬X). If it outputs Y, it expects to get utility E(v|X)-c (because of the -c penalty).

Therefore (ignoring ties) M(v#) will output Y iff it estimates Q(v,X,c) to be true. And, since in actual fact Z=0 almost certainly, we get to see its output, hence its conclusion. Voila!

Note: the advantage of this method is to allow us to get the truth out of an AI, without knowing how to define "truth".

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