maspushagent using CPU [retina MacBook Pro 15", Late 2013, OS X 10.11.4]

I always keep Activity Monitor running, and just noticed that CPU usage was up significantly. The process maspushagent (owned by me) has now been running at ~123% CPU for close to an hour now. The requisite googling doesn't turn up anything useful. What does this do, and will it quit any time soon, or should I kill/reboot/?
The maspushagent is the "push agent" for the "Mac App Store". Being a "push agent" means that it used for receiving/processing notifications from Apple's servers. It could for example be notifications about an update.

The program is automatically started by launchd when a notification is received by the Mac destined for the Mac App Store.

Therefore it should be safe to simply kill the mapushagent if it is behaving like you describe. Hopefully that fixes the issue for you.