Jessica Taylor. CS undergrad and Master’s at Stanford; former research fellow at MIRI.
I work on decision theory, social epistemology, strategy, naturalized agency, mathematical foundations, decentralized networking systems and applications, theory of mind, and functional programming languages.
Blog: unstableontology.com
Twitter: https://twitter.com/jessi_cata
Ok, we could set up the game so that the input string is a uniformly random element of the finite set , and for is the probability of one-boxing when the input is , where parameters are . The action is which is distributed according to . The reward is .
It might depend what the network actually is, but in the simple case, gives the probability of one-boxing for each input separately.
Again we consider REINFORCE with a huge N. We get an approximate uniform sampling from . Actually, due to how we defined the network, we only make updates to the components of independently; the component of is only affected by runs for which . Now once we focus attention on the updates to the component of , we are looking at something that is, up to a scaling factor, the same thing as running REINFORCE on Newcomb’s problem but without the string . Now the argument from before applies: REINFORCE is going to act like CDT, because controlling for and , runs which two-box have more reward.
In conclusion, under this setup, REINFORCE is going to act like CDT. There is some possible variation in how to lay out the network (I made the simplifying assumption here), though I’m guessing for a sufficiently big network, able to encode “practically all” functions , the empirical results would be similar. (And as before, I am guessing PPO is like REINFORCE since it’s an importance sampling adjustment)