The maximum is over the domain. I’m not sure how your example is escaping from the hierarchy paradigm. I do consider the idea of having undetermined sub-tasks.
When we make plans we oftentimes will create tasks that themselves require further planning. It seems perfectly reasonable that we could simply “call” our meta-plan on these sub-tasks to reduce the effect of human bias.
You seem concerned about why I choose to characterize the policy by how well it compresses the task. While it was possible to do a sort of ‘interleaving’ as you suggest from a technical point of view it makes no difference since compression transitions are assumed to be Markov. This translates to an assumption that planning ability depends only on what you currently have planned.
Practically speaking I should assume that the transitions are Markov and depend on both what has been planned and what has been executed. My argument rests on the idea that in expectation there’s no difference between the two strategies since what you plan for will in expectation match what happens.
The moment you start trying to build up a more complicated model it becomes clear that you can’t simply account for what has been executed in terms of a scalar. Otherwise what I just said is reinforced. In that case, you need to model how tasks are being created, prioritized, and executed. This is difficult to the point of being useless as a tool to understand what I was interested in.
I think we agree that the only way forward is to simply assume that this ‘meta’-policy can be invoked recursively. This is hard. Naively I’d hope for sub-task modularity/independence and additivity of the effectiveness ‘meta’-policy.
π=π1π2=π2π1
Γ(π)=Γ(π1)+Γ(π2)
Hopefully, it’s clearer why it’s impossible to go further without a good model for how tasks are sub-divided. It’s all too easy to run into Zeno-like paradoxes where it’s either impossible to plan due to compounding sub-task over-head or you can slice-up a task into infinitesimal dust. This is getting too long for a comment. I’ll leave it there.
I should have split things up into multiple comments. Most (if not all) of that should be read as “I think this might be useful in practice* for planning/executing, rather than improving the model”.
*Advice which if followed would or could have led to a) doing LaTex sooner, b) changed how math was handled or turned out, or making it less unpredictable w.r.t to time estimates, c) formatting the writing sooner.
Hopefully, it’s clearer why it’s impossible to go further without a good model for how tasks are sub-divided.
I suggested
1) that if writing the math* was a substantial piece which took longer than expected, then you might find it useful to have a personal model which says “Math* will take longer than I expect”/update future expectations based on the result—how things turned out for this post.
2) If you change the way you divide up tasks that might affect outcomes**, if not predictability.
*Or anything else this applies to.
**Such as how long things take, as well as how they turn out.
The maximum is over the domain. I’m not sure how your example is escaping from the hierarchy paradigm. I do consider the idea of having undetermined sub-tasks.
You seem concerned about why I choose to characterize the policy by how well it compresses the task. While it was possible to do a sort of ‘interleaving’ as you suggest from a technical point of view it makes no difference since compression transitions are assumed to be Markov. This translates to an assumption that planning ability depends only on what you currently have planned.
Practically speaking I should assume that the transitions are Markov and depend on both what has been planned and what has been executed. My argument rests on the idea that in expectation there’s no difference between the two strategies since what you plan for will in expectation match what happens.
The moment you start trying to build up a more complicated model it becomes clear that you can’t simply account for what has been executed in terms of a scalar. Otherwise what I just said is reinforced. In that case, you need to model how tasks are being created, prioritized, and executed. This is difficult to the point of being useless as a tool to understand what I was interested in.
I think we agree that the only way forward is to simply assume that this ‘meta’-policy can be invoked recursively. This is hard. Naively I’d hope for sub-task modularity/independence and additivity of the effectiveness ‘meta’-policy.
π=π1π2=π2π1
Γ(π)=Γ(π1)+Γ(π2)
Hopefully, it’s clearer why it’s impossible to go further without a good model for how tasks are sub-divided. It’s all too easy to run into Zeno-like paradoxes where it’s either impossible to plan due to compounding sub-task over-head or you can slice-up a task into infinitesimal dust. This is getting too long for a comment. I’ll leave it there.
I should have split things up into multiple comments. Most (if not all) of that should be read as “I think this might be useful in practice* for planning/executing, rather than improving the model”.
*Advice which if followed would or could have led to a) doing LaTex sooner, b) changed how math was handled or turned out, or making it less unpredictable w.r.t to time estimates, c) formatting the writing sooner.
I suggested
1) that if writing the math* was a substantial piece which took longer than expected, then you might find it useful to have a personal model which says “Math* will take longer than I expect”/update future expectations based on the result—how things turned out for this post.
2) If you change the way you divide up tasks that might affect outcomes**, if not predictability.
*Or anything else this applies to.
**Such as how long things take, as well as how they turn out.