Intelligent Agent Foundations Forumsign up / log in
An implementation of modal UDT
post by Benja Fallenstein 1013 days ago | Jessica Taylor, Luke Muehlhauser, Nate Soares and Patrick LaVictoire like this | discuss

One of the great advantages of working with Gödel-Löb provability logic is that it’s possible to implement an evaluator which efficiently checks whether a sentence in the language of GL is true. Mihaly and Marcello used this to write a program that checks whether two modal agents cooperate or defect against each other. Today, Nate and I extended this with an implementation of modal UDT, which allows us to check what UDT does on different decision problems—see Program.hs in the Github repository. No guarantees for correctness, since this was written rather quickly; if anybody is able to take the time to check the code, that would be very much appreciated!


The implementation of UDT is rather pleasing, I think. Here’s the informal definition of modal UDT, using PA + \(\ell\):

  • For every possible outcome \(j\), from best to worst:
    • For every possible action \(i\), in order:
      • If it’s provable in PA + \(\ell\) that “UDT takes action \(i\)” implies “the universe returns outcome \(j\)”, then take action \(i\).
  • If you’re still here, return a default action.

Here is the corresponding Haskell code:

udt :: (Enum a,Ord b,Show b,Enum b)
    => Int -> ModalProgram b a -> b -> ModalProgram b b
udt level univ dflt = modalProgram dflt $
  mFor $ \a ->
    mFor $ \b ->
      mIf (boxk level (Var b %> univ a)) (mReturn b)

Being able to write modal UDT like this makes it very easy to implement and try small variations on the code.


We used this code to check what modal UDT would do in a version of Newcomb’s problem where Omega uses proofs in PA (rather than simulations) to decide whether to put the money in the box; that is, it will put a million dollars in the first box if and only if it can prove that you will one-box. If our code is correct, it turns out that in this case, modal UDT will do whatever its default action was.

Earlier, we thought we had proved a different result on the whiteboard, but after the code disagreed with us, we went over it again and found a bug in our proof. After fixing that bug, we now have a manual proof that UDT will end up taking its default action in this scenario (which I’ll write about some other time). So looks like this can be a useful tool for figuring out this sort of thing!



NEW LINKS

NEW POSTS

NEW DISCUSSION POSTS

RECENT COMMENTS

Unfortunately, it's not just
by Vadim Kosoy on Catastrophe Mitigation Using DRL | 0 likes

>We can solve the problem in
by Wei Dai on The Happy Dance Problem | 1 like

Maybe it's just my browser,
by Gordon Worley III on Catastrophe Mitigation Using DRL | 2 likes

At present, I think the main
by Abram Demski on Looking for Recommendations RE UDT vs. bounded com... | 0 likes

In the first round I'm
by Paul Christiano on Funding opportunity for AI alignment research | 0 likes

Fine with it being shared
by Paul Christiano on Funding opportunity for AI alignment research | 0 likes

I think the point I was
by Abram Demski on Predictable Exploration | 0 likes

(also x-posted from
by Sören Mindermann on The Three Levels of Goodhart's Curse | 0 likes

(x-posted from Arbital ==>
by Sören Mindermann on The Three Levels of Goodhart's Curse | 0 likes

>If the other players can see
by Stuart Armstrong on Predictable Exploration | 0 likes

Thinking about this more, I
by Abram Demski on Predictable Exploration | 0 likes

> So I wound up with
by Abram Demski on Predictable Exploration | 0 likes

Hm, I got the same result
by Alex Appel on Predictable Exploration | 1 like

Paul - how widely do you want
by David Krueger on Funding opportunity for AI alignment research | 0 likes

I agree, my intuition is that
by Abram Demski on Smoking Lesion Steelman III: Revenge of the Tickle... | 0 likes

RSS

Privacy & Terms