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flashfaffe2 4 days ago [-]
Thanks for the refreshing reminder.
This was one of my favourite topic at school but ended never used it in professional environment. However , I will definitely review the theory. Banach spaces and fix theorem were kind useful definition/tool but I always struggled to understand practical applications.
Thanks for sharing the article
kooi 10 hours ago [-]
Agreed, very cool article.
> I always struggled to understand practical applications.
Me too...and specifically with non-smooth dynamical systems. I always felt some better knowledge or intuition on my part could lead to understanding the practical application.
It's one reason I left academia... wtf this is cool, but wtf is this useful for?
The closest practical application I can fathom in this theoretical realm is optimization. And welp, since that underlies all AI, that's pretty important. Oh and cryptography.
inigyou 8 hours ago [-]
I was pretty sure the "dynamic" in "dynamic programming" was used as a synonym for "awesome" and had nothing to do with system dynamics.
abetusk 6 hours ago [-]
[0]:
> ... I thought dynamic programming was a good name. It was something not even a Congressman could object to. So I used it as an umbrella for my activities.
>Proof: It all follows from applying the Banach fixed point theorem to the Bellman operator.
I disagree. When people hate mathematicians, it's because of things like this.
Why? Because it doesn't follow exclusively from the things listed. It also follows from the fact that c, T, A are bounded by the problem definition. Variable names in math confer no meaning, you can choose any variable name, hence you could have chosen an optimization problem that has no unique solution, simply out of spite.
Now the counter to that is that the introduction covered the restrictions on c, A and T but why drop them in the proof?
ahahs 5 hours ago [-]
side note: refreshing to read non ai articles
deterministic 2 days ago [-]
Thanks! What a great read.
LoganDark 4 hours ago [-]
> An optimal policy has the property that whatever the initial state and initial decision are, the remaining decisions must constitute an optimal policy with regard to the state resulting from the first decision.
So an optimal policy is an optimal policy. Got it.
kikimora 56 minutes ago [-]
You have n decisions to make - this is your policy. After you make one, if your remaining n-1 decisions also optimal, then you have optimal policy.
LoganDark 24 minutes ago [-]
So, an optimal policy is basically one that does not put you into a suboptimal position?
Thanks for sharing the article
> I always struggled to understand practical applications.
Me too...and specifically with non-smooth dynamical systems. I always felt some better knowledge or intuition on my part could lead to understanding the practical application.
It's one reason I left academia... wtf this is cool, but wtf is this useful for?
The closest practical application I can fathom in this theoretical realm is optimization. And welp, since that underlies all AI, that's pretty important. Oh and cryptography.
> ... I thought dynamic programming was a good name. It was something not even a Congressman could object to. So I used it as an umbrella for my activities.
[0] https://en.wikipedia.org/wiki/Dynamic_programming#History_of...
I disagree. When people hate mathematicians, it's because of things like this.
Why? Because it doesn't follow exclusively from the things listed. It also follows from the fact that c, T, A are bounded by the problem definition. Variable names in math confer no meaning, you can choose any variable name, hence you could have chosen an optimization problem that has no unique solution, simply out of spite.
Now the counter to that is that the introduction covered the restrictions on c, A and T but why drop them in the proof?
So an optimal policy is an optimal policy. Got it.