Maybe it is possible to add apps to whitelist in a future?

I saw this implementation in Sony Xperia. I will explain why. Now I am using SGS4 I9505 running 4.4.2. I have Google Play Music Unlimited subscription. So, I am listening music with streaming option, screen goes off and after some time avast! Battery Saver turns off my data connection and no music left. I know, the option is to turn off Battery Saver, but it is so inconvenient...
