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  > gradient descent isn't good at combinatorial optimisation.
If you convolve your problem with sufficiently wide Gaussian, you can use gradient descent. The approach is called Natural Evolution Strategies [1].

[1] https://en.wikipedia.org/wiki/Natural_evolution_strategy#Nat...

It requires O(N^4) evaluations to compute Fisher Information Matrix for N-dimensional parameterization of the problem in original formulation. But there are closed form solutions and more economical representations of covariance matrix (LoRA, hehe).



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