Summary

I present an extension to my optimal timing of spending on AGI safety model for calculating the value of information of AGI timelines via informing one’s spending schedule.

I show, using my best guess of the model parameters, that for an AI risk funder uncertain between a ‘short timelines’ model and ‘medium timelines’ model:

Updating from near certainty in medium timelines to short timelines (and following the new optimal spending strategy) leads to a 40% increase in utility.
Updating from near certainty in short timelines to medium timelines (and following the new optimal spending strategy) leads to a 20% increase in utility.

The gains are greater when considering a model of the community’s capacity, rather than capital.

I also show that small changes in one’s credence in short or medium timelines has relatively little impact on one’s optimal spending schedule, especially when one starts out with roughly equal credence in each^[1].

You can enter your own parameters - such as AGI timelines, discount rate and diminishing returns to spending - here.

In an appendix I apply a basic model to consider the opportunity cost of timelines work. This model does not assume novel research is done.

The setup

Suppose you have two ‘models’ of AGI timelines $A$ and $B$ , with credence $p_{A}$ in $A$ and $(1 - p_{A})$ in $B$ ^[2]. You use your mixture distribution for AGI timelines $p_{A} \cdot A + (1 - p_{A}) \cdot B$ to calculate the optimal spending schedule for AI risk interventions.

You could do some thinking and come to some credence $p_{A}^{'}$ in $A$ and $(1 - p_{A}^{'})$ in $B$ . How much better is the optimal spending schedule as a result of $p_{A}^{'}$ to the optimal spending schedule as a result of $p_{A}$ , both supposing $p_{A}^{'}$ ?

Writing $S_{p_{A}}$ for optimal spending schedule according to $p_{A}$ and $U (S_{p_{A}} | p_{A})$ for utility of $S_{p_{A}}$ supposing $P_{A}$ , I compare $U (S_{p_{A}^{'}} | p_{A}^{'})$ to $U (S_{p_{A}} | p_{A}^{'})$ (the former, by definition of optimality is greater or equal to the latter).

In the model, utility is the discount adjusted probability we ‘succeed’ with making AGI go well. The maximum utility is $\int_{0}^{t} p (t) \cdot e^{- δ t} d t \leq 1$ where $p (t)$ are the AGI timelines and $d$ is the discount rate.

Example results for short and medium timelines

I take $A$ and $B$ as the followin...

Optimal spending for ai risk