This seems potentially very interesting, but I’m not totally sure I see where it’s going?
What are the fitting parameters of this model? The mean of D? If I want to compare investing in FAI to fusion, how does this improve my previous “X seems on average easier” heuristic? Are there any real life examples that we could apply this model to?
Random asides:
I’m not totally sold on the reasoning for choosing the Pareto distribution. Why would I expect problem difficulty to follow a Pareto distribution? Is there any set of solved problems for which that has been true?
This seems vaguely reminiscent of the multi-armed bandit problem, although the payoffs in your formulation are entirely binary. Is a binary Success/Failure a realistic model of technical progress? Can the existing research on k-armed bandits be applied to this type of problem?
I’m going to reply briefly to some of these questions, but the subject of several of them should be more comprehensively covered in future posts.
Yes, I will be applying this model (& extensions) to some real examples, and also looking at some places where it predicts observed behaviour.
Yes, binary success/failure is not always a good model, and I’ll explore this.
Fallenstein and Mennen give more in-depth justifications for why you might use a Pareto distribution in the linked article; I wasn’t really defending the Pareto distribution, so perhaps I passed over this rather quickly.
Interesting idea on analogies with the multi-armed bandit problem. My impression is that it’s not really applicable, since we’re looking at problems which only pay out once (or at the very least have diminishing returns), but there might be something to say there. I’ll think about it.
This seems potentially very interesting, but I’m not totally sure I see where it’s going?
What are the fitting parameters of this model? The mean of D? If I want to compare investing in FAI to fusion, how does this improve my previous “X seems on average easier” heuristic? Are there any real life examples that we could apply this model to?
Random asides:
I’m not totally sold on the reasoning for choosing the Pareto distribution. Why would I expect problem difficulty to follow a Pareto distribution? Is there any set of solved problems for which that has been true?
This seems vaguely reminiscent of the multi-armed bandit problem, although the payoffs in your formulation are entirely binary. Is a binary Success/Failure a realistic model of technical progress? Can the existing research on k-armed bandits be applied to this type of problem?
I’m going to reply briefly to some of these questions, but the subject of several of them should be more comprehensively covered in future posts.
Yes, I will be applying this model (& extensions) to some real examples, and also looking at some places where it predicts observed behaviour.
Yes, binary success/failure is not always a good model, and I’ll explore this.
Fallenstein and Mennen give more in-depth justifications for why you might use a Pareto distribution in the linked article; I wasn’t really defending the Pareto distribution, so perhaps I passed over this rather quickly.
Interesting idea on analogies with the multi-armed bandit problem. My impression is that it’s not really applicable, since we’re looking at problems which only pay out once (or at the very least have diminishing returns), but there might be something to say there. I’ll think about it.