Given a world model ν, which takes k computation steps per episode, let νlog be the best world-model that best approximates ν (in the sense of KL divergence) using only logk computation steps.νlog is at least as good as the “reasoning-based replacement” of ν.
The description length of νlog is within a (small) constant of the description length of ν. That way of describing it is not optimized for speed, but it presents a one-time cost, and anyone arriving at that world-model in this way is paying that cost.
One could consider instead νlogε, which is, among the world-models that ε-approximate ν in less than logk computation steps (if the set is non-empty), the first such world-model found by a searching procedure ψ. The description length of νlogε is within a (slightly larger) constant of the description length of ν, but the one-time computational cost is less than that of νlog.
νlog, νlogε, and a host of other approaches are prominently represented in the speed prior.
If this is what you call “the speed prior doing reasoning,” so be it, but the relevance for that terminology only comes in when you claim that “once you’ve encoded ‘doing reasoning’, you’ve basically already written the code for it to do the treachery that naturally comes along with that.” That sense of “reasoning” really only applies, I think, to the case where our code is simulating aliens or an AGI.
(ETA: I think this discussion depended on a detail of your version of the speed prior that I misunderstood.)
Given a world model ν, which takes k computation steps per episode, let νlog be the best world-model that best approximates ν (in the sense of KL divergence) using only logk computation steps. νlog is at least as good as the “reasoning-based replacement” of ν.
The description length of νlog is within a (small) constant of the description length of ν. That way of describing it is not optimized for speed, but it presents a one-time cost, and anyone arriving at that world-model in this way is paying that cost.
To be clear, that description gets ~0 mass under the speed prior, right? A direct specification of the fast model is going to have a much higher prior than a brute force search, at least for values of β large enough (or small enough, however you set it up) to rule out the alien civilization that is (probably) the shortest description without regard for computational limits.
One could consider instead νlogε, which is, among the world-models that ε-approximate ν in less than logk computation steps (if the set is non-empty), the first such world-model found by a searching procedure ψ. The description length of νlogε is within a (slightly larger) constant of the description length of ν, but the one-time computational cost is less than that of νlog.
Within this chunk of the speed prior, the question is: what are good ψ? Any reasonable specification of a consequentialist would work (plus a few more bits for it to understand its situation, though most of the work is done by handing it ν), or of a petri dish in which a consequentialist would eventually end up with influence. Do you have a concrete alternative in mind, which you think is not dominated by some consequentialist (i.e. a ψ for which every consequentialist is either slower or more complex)?
Do you have a concrete alternative in mind, which you think is not dominated by some consequentialist (i.e. a ψ for which every consequentialist is either slower or more complex)?
Well one approach is in the flavor of the induction algorithm I messaged you privately about (I know I didn’t give you a completely specified algorithm). But when I wrote that, I didn’t have a concrete algorithm in mind. Mostly, it just seems to me that the powerful algorithms which have been useful to humanity have short descriptions in themselves. It seems like there are many cases where there is a simple “ideal” approach which consequentialists “discover” or approximately discover. A powerful heuristic search would be one such algorithm, I think.
(ETA: I think this discussion depended on a detail of your version of the speed prior that I misunderstood.)
I don’t think anything here changes if K(x) were replaced with S(x) (if that was what you misunderstood).
Given a world model ν, which takes k computation steps per episode, let νlog be the best world-model that best approximates ν (in the sense of KL divergence) using only logk computation steps.νlog is at least as good as the “reasoning-based replacement” of ν.
The description length of νlog is within a (small) constant of the description length of ν. That way of describing it is not optimized for speed, but it presents a one-time cost, and anyone arriving at that world-model in this way is paying that cost.
One could consider instead νlogε, which is, among the world-models that ε-approximate ν in less than logk computation steps (if the set is non-empty), the first such world-model found by a searching procedure ψ. The description length of νlogε is within a (slightly larger) constant of the description length of ν, but the one-time computational cost is less than that of νlog.
νlog, νlogε, and a host of other approaches are prominently represented in the speed prior.
If this is what you call “the speed prior doing reasoning,” so be it, but the relevance for that terminology only comes in when you claim that “once you’ve encoded ‘doing reasoning’, you’ve basically already written the code for it to do the treachery that naturally comes along with that.” That sense of “reasoning” really only applies, I think, to the case where our code is simulating aliens or an AGI.
(ETA: I think this discussion depended on a detail of your version of the speed prior that I misunderstood.)
To be clear, that description gets ~0 mass under the speed prior, right? A direct specification of the fast model is going to have a much higher prior than a brute force search, at least for values of β large enough (or small enough, however you set it up) to rule out the alien civilization that is (probably) the shortest description without regard for computational limits.
Within this chunk of the speed prior, the question is: what are good ψ? Any reasonable specification of a consequentialist would work (plus a few more bits for it to understand its situation, though most of the work is done by handing it ν), or of a petri dish in which a consequentialist would eventually end up with influence. Do you have a concrete alternative in mind, which you think is not dominated by some consequentialist (i.e. a ψ for which every consequentialist is either slower or more complex)?
Well one approach is in the flavor of the induction algorithm I messaged you privately about (I know I didn’t give you a completely specified algorithm). But when I wrote that, I didn’t have a concrete algorithm in mind. Mostly, it just seems to me that the powerful algorithms which have been useful to humanity have short descriptions in themselves. It seems like there are many cases where there is a simple “ideal” approach which consequentialists “discover” or approximately discover. A powerful heuristic search would be one such algorithm, I think.
I don’t think anything here changes if K(x) were replaced with S(x) (if that was what you misunderstood).