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EdisonCruise
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Re: Why is Bellman Equation solved by backwards?

October 15th, 2019, 3:10 am

Thank you katastrofa. I think your explanation make sense.
 
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JohnLeM
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Re: Why is Bellman Equation solved by backwards?

October 15th, 2019, 12:25 pm

Thank you all, but I what I cannot understand is the real reason that Bellman equation is ususally solved by backwards. Can any one give an exmaple in which both intitial and terminal conditions are well defined, but the Bellman equation can only be solved by backwards?
I think there are tons of examples, the most proeminent being the backward heat equation [$]\partial_t u = -\Delta u[$], that fits Bellman framework AFAIR. The reason is that these kind of equations dissipate some entropy : you loose informations at each time, preventing you from going back forward to your initial state.
By the way sometimes the Bellman equations are forward, depends on example. For instance Burgers equations are forward Bellman ones (to be precise, burgers equations fits the Jacobi-Bellman framework). Due to entropy dissipation, you can't move them backwards.
 
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Paul
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Re: Why is Bellman Equation solved by backwards?

October 15th, 2019, 3:46 pm

At last, an actual equation! Going the wrong direction in time is an ill-posed problem. You cannot tell the original distribution of smoke in a room. Try it. Write a short diffusion equation finite difference solver and experiment with changing the sign of diffusion.

Thank you, JohnLeM, this thread had been painful to watch before!
 
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katastrofa
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Re: Why is Bellman Equation solved by backwards?

October 15th, 2019, 4:07 pm

Time is an ill-posed concept, burger lover!
 
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Cuchulainn
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Re: Why is Bellman Equation solved by backwards?

October 15th, 2019, 8:09 pm

Time is an ill-posed concept
Time is what keeps everything from happening at once.
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Paul
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Re: Why is Bellman Equation solved by backwards?

October 15th, 2019, 8:40 pm

It's astounding
 
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katastrofa
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Re: Why is Bellman Equation solved by backwards?

October 15th, 2019, 9:52 pm

Everything's already happened!
 
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Paul
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Re: Why is Bellman Equation solved by backwards?

October 16th, 2019, 1:32 am

...is fleeting
 
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katastrofa
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Re: Why is Bellman Equation solved by backwards?

October 16th, 2019, 5:43 am

Everything is alright with time... assuming the second law of thermodynamics holds... assuming the concept of randomness is correct... because according to its definition it exists only in the infinite limit of time... Just teasing you. Sorry!
 
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Cuchulainn
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Re: Why is Bellman Equation solved by backwards?

October 16th, 2019, 6:35 am

Time flies like an arrow; fruit flies like a banana
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katastrofa
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Re: Why is Bellman Equation solved by backwards?

October 16th, 2019, 7:19 am

Westerners are more attached to the notion of time than people in the East, where many don't even know their birthdate. Not to mention Africa. (A fun fact: if you look at the data on people even as young as 30 from some Middle Eastern country, you sometimes can see suspicious spikes, e.g. on 1 Jan - they or the admin simply put an easy to remember date as their birthday if they didn't know it. I'm an extreme case of it - I got the same, incorrect, birth year as the rest of the children when I started the school, because it was the first occasion it was needed; when I changed schools skipping one year, I again got the same year of birth as other children's while for the day and month my Polish grandma chose her the name day  - she used to say that I was a present for her. (In Poland they have each day of calendar year attributed to some first name and celebrated it more than birthdays at the time.)
That's why I stopped wasting my time on people from the West :-)
 
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Cuchulainn
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Re: Why is Bellman Equation solved by backwards?

October 16th, 2019, 1:16 pm

The more erudite Wilmott readers will know the Vico theory of time and that it moves in cycles. I've said it often enough.
(Paul; Cycle 3 is democracy, which we are now leaving and going into Cycle 1 which will please some people).

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katastrofa
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Re: Why is Bellman Equation solved by backwards?

October 17th, 2019, 12:33 am

I'm afraid you're the only erudite here, Cuchulainn. Or are there any other old Irish expat fanatics of (the) Joyce here?

Isn't it that in the past people believed in the cycles (in Indian lingam-yoni, Chinese yin-yang or baba-jaga in Ukrainian mythology), and today we think of transitions?

What kicked us out of the balance? Or we were simply wrong: "The more we know about our universe, the more difficult it becomes to believe in determinism", Prigogine, 1997?
 
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Paul
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Re: Why is Bellman Equation solved by backwards?

October 17th, 2019, 2:28 am

I’ll have what she’s smoking.
 
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katastrofa
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Re: Why is Bellman Equation solved by backwards?

October 17th, 2019, 2:46 am

That's my nervous reaction to Cuchulainn and JLM's ramblings about the universal approximation theorem.
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