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Jules Hedges (Mar 24 2020 at 15:06):There is a little, but not much. This is one of the main things I'm thinking about. Michael Johnson did a bunch of related things. There is also a paper on MDPs viewed coalgebraically by Helle Hansen et al
Jules Hedges (Mar 24 2020 at 15:10):My explorations in "everything is lenses" has quite a lot to say about optimisation, I think
Jules Hedges (Mar 24 2020 at 15:11):If I could set one question in this area: People sometimes talk about "Kalman duality", can it be formalised in the usual settings of duality theory?
Georgios Bakirtzis (Mar 24 2020 at 15:11):I am particularly interested in what category theory can say about the following problem where with constraints ,
Georgios Bakirtzis (Mar 24 2020 at 15:15):In general, my questions in optimization and particularly optimal control and category theory is can we come up with a better algorithm using a categorical formulation a la UMAP?
Georgios Bakirtzis (Mar 24 2020 at 15:15):Don't really know where to start though.
Philip Zucker (Mar 24 2020 at 16:43):I was fiddling in a related area recently. http://www.philipzucker.com/categorical-combinators-for-convex-optimization-and-model-predictive-control-using-cvxpy/ There's at least one way in which optimization problems can be considered compositionally, compising by summing objectives and using minimization of the interior variables rather than just existentializing them out as in Rel. We swap one binding form for another. I've had a suspicion for a long while that the ADMM algorithm has a strong lensy flavor to it with a forward pass minimizing and the backward pass updating dual variables? I don't have this quite nailed down. ADMM feels like some kind of relative of backprop.