Automatic Differentiation Applications to Planning?
I've been working with automatic differentiation in my research and was wondering if there's any application towards planning? I know it's been used to accelerate linear solvers but I'm wondering if it can be used to accelerate linear programming?
What exactly would be differentiated? It's already known that predictor-corrector methods for LP are fast.
You'd differentiate with respect to some variable parameters of a solver for GD-based optimization of that parameter with respect to some target
I don't know the extent to which this would be useful but just to illustrate you could differentiate plan outputs with respect to technical coefficients.
Maybe other mathematical programming paradigms could make better use AutoDiff?
Sounds similar to a thing in LP theory known as the pillmaker's problem. With LPs small enough that they can be solved exactly, an optimal solution consists of a basis which gives you this kind of information. Only coefficients contained in that basis can affect the solution. With interior points the situation is trickier, but you can certainly ask questions like "what happens if we bring in more productive machinery in industry X?"