You can relax the problem in order to reduce complexity and calculations. For example: cut the training of slow learning networks, have a database of already trained networks, decrease the number of epochs and examples, etc. Or even create another network which predicts the convergence of a network and use it as heuristic. If you also take into account the size of the network and force the learning to minimize them, then you can train them faster.

We cannot do it at home, but for sure Google can try it in their servers.