Predicting the performance of deep learning models

It's widely acknowledged that the recent successes of Deep Learning rest heavily upon the availability of huge amounts of data. Vision was the first domain in which the promise of DL was realised, probably because of the availability of large datasets such as ImageNet. The recent surge of simulators for RL further illustrates that as we push further to apply these techniques to real-world problems, data scarcity quickly becomes the bottleneck. In commercial contexts, this question comes up a lot. When time and money is at stake, it'd be useful to be able to make some concrete statements about how improvements in model architecture are likely to weigh up against simply gathering more data.