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blockspins's profile
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@blockspins

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@blockspins

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    1. julesh‏ @_julesh_ 26 Sep 2019
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      For fun I spent an hour seriously thinking about sheaves of open games. I got way over my head very, very quickly - and that's not even getting to the part with the sheaves or the other part with the PDEs

      1 reply 1 retweet 17 likes
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    2. julesh‏ @_julesh_ 26 Sep 2019
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      Basically the simplest possible example (with one player and time as the base space) is the Hamilton-Jacobi-Bellman equation. Which, so far, I'm failing to get my head around

      4 replies 0 retweets 7 likes
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    3. Philip Zucker‏ @SandMouth 26 Sep 2019
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      Replying to @_julesh_

      Difficulty to interpret as a sheaf or to intuitively grasp in it‘s own right?

      1 reply 0 retweets 0 likes
    4. julesh‏ @_julesh_ 26 Sep 2019
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      Replying to @SandMouth

      Just trying to understand the thing itself. If I'm thinking about open games in the right way then I think it will either automatically be a sheaf, or (probably equally likely) the whole thing is a bust

      2 replies 0 retweets 0 likes
    5. Philip Zucker‏ @SandMouth 26 Sep 2019
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      Replying to @_julesh_

      Have you considered the discrete state space version or do you really need the continuous PDE? The PDE form is rather confusing to me. The discrete Bellman equation feels clever but reasonable and has the PDE as a limitting case.

      1 reply 0 retweets 1 like
    6. julesh‏ @_julesh_ 26 Sep 2019
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      Replying to @SandMouth

      Ah, that's a good idea, maybe I should look at discrete space continuous time first, that sounds way easier if it's a standard thing

      2 replies 0 retweets 1 like
    7. bgc‏ @blockspins 26 Sep 2019
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      Replying to @_julesh_ @SandMouth

      Sadly, Kohn and Serfaty use continuous space, discrete time. It would be interesting to see something written the other way around though!

      1 reply 0 retweets 1 like
    8. Philip Zucker‏ @SandMouth 26 Sep 2019
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      Replying to @blockspins @_julesh_

      Is kohn and serfaty a mental touch stone? I’m not familiar with it

      1 reply 0 retweets 0 likes
      bgc‏ @blockspins 26 Sep 2019
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      Replying to @SandMouth @_julesh_

      bgc Retweeted bgc

      Ah, sorry, see this tweet elsewhere in this thread treehttps://twitter.com/blockspins/status/1177274861644918787 …

      bgc added,

      bgc @blockspins
      Replying to @_julesh_
      As an outsider to games and control, I thought the formal derivations in this expository paper by Kohn and Serfaty were illuminating: https://www.math.nyu.edu/faculty/kohn/papers/kohn-serfaty-iciam.pdf … (I'm not sure if this is what you have in mind and apologies if you already know this paper!)
      11:14 AM - 26 Sep 2019
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