Is there any software that can do geometry optimization using machine learning?
There is one Python package that I know: AMP (Atomistic Machine-learning Package). It is based on ASE (Atomic Simulation Environment), a homogeneous interface to a lot of computational chemistry packages.

Basically, after you obtain geometry trajectories through ASE (using any computational chemistry package you like), an approximation to the potential energy surface (PES) is machine-learned. It can be used as an ASE interface.

You can theoretically do anything ASE is capable of with this, from saddle point optimization to quantum dynamics.
I am not an expert in this field, but they seem to apply ideas from convolutional neural networks to molecular structures for describing the chemical environment surrounding atoms.
Their method is described in Khorshidi, A.; Peterson, A. A. Amp: A Modular Approach to Machine Learning in Atomistic Simulations. Computer Physics Communications 2016, 207, 310–324.