alt Hacker NewsFeels to me like there is no need for backpropagation. I think you can just iteratively grab a random pixel and flip it of that would bring you closer to the target after one step.
It would probably work even better if you tweak the loss function with some kind of averaging/blurring filter.
This is just the brute force solution. I'm pretty sure that's no more efficient than guessing all pixels at once and trying to check of that worked or not.