Algorithms for making neural nets converge

I am currently using a simple PID, and I was wondering if there's a faster one.
I know about backpropagation, genetic/evolutionary algorithms and steepest/conjugate gradient descent, but they all seem to me just fancy ways of doing PID and I can never get them to work better than PID, which really demotivates implementing them any further.
Still, I hate how slow the convergence is, so I was wondering if there's some sort of magic algorithm someone here knows about. (linear/superlinear convergence? I wish)

>>2
I'm just a hobbyist playing around trying to make bots for games and such silly stuff.
I already found out that PID actually gives (nearly) linear convergence on certain activation functions (it was just that I was using bad activation functions that websites tell me to use and not my own).
However, I would like to know about these better learning algorithms.
Can you also explain SVM to me in a simple way? I will also look more into it.