A full solution to the extortion problem is sorely elusive. However, there are crude hacks that we can use to mitigate the downside.
Suppose we figured out that a friendly AI should be maximising an unbounded utility function U. The extortion risk is that another AI could threaten a FAI with unbounded disutility if it didn't go along with its plans. This gives the extorting AI -- the EAI -- a lot of leverage, and things could end up badly if the EAI ends up acting on its threat.
To combat this, we first have to figure out a level z of utility that is a lower bound on what U could ever reach naturally and realistically.
By "naturally" we mean that U going below z would require not just incompetence or indifference, but some AI actively and deliberately arranging the lowering of U. And "realistically" just means that we're confident that getting U lower than z by chance, or having a U-minimising AI, are exceedingly low.
Then what we can do is to cut off U at the z level, replacing U with U′=max(U,U(z)). See z indicated by the red line on this graph of U′ versus U:
What's the consequence of this? First of all, it ensures that no EAI would threaten to reduce U (the utility we really care about) below z, because that is not a threat to the FAI. This reduces the leverage of the EAI, and reduces the impact of it acting on its threat.
Since levels of U below z are exceedingly unlikely to happen by chance, the fact the FAI has the wrong utility below z shouldn't affect it's performance much. And, even in that zone, the AI is still motivated to climb U above z.
But we may still feel unhappy about the flatness of that curve, and want it to still prefer higher U to exceedingly low values. If so, we can replace U with U′′ as follows:
In this case, the EAI will not seek to reduce U below z−1 (in fact, it will specifically target that value), while the FAI has the correct ordering of lower values of U. The utility is weird around z, granted, but this is a place where the FAI would not want to be and would almost certainly not reach by accident.
Though this method does not eliminate the threat of extortion, it does seem to reduce its impact.
I am a little confused by the axes on those graphs. Is utility meant to decrease from left to right (inverting the x axis) and to increase from bottom to top (normal y axis)?
Ah yes, that was an error. I've flipped the graphs now.
This doesn't seem to me to work. It seems the FAI's best reaction is simply to not grow above b until it's sure the EAI can't mess it up, rather than changing it's own values to ensure the same result.
Ah, but we would like an infinite carrot :-) And cutting off U at the top would (almost) guarantee that we don't get higher utility.