Update to iOS 11.2 if you have a backup or can connect to iTunes and update over USB.
Try to turn off app notifications if you can get to settings and disable them one by one in between "resprings"
Once local notifications are off, you should have a stable phone to then make a backup or plan for an update / patch or remove the offending apps.
Apparently this is happening for many people in Japan since midnight. Reports from Australia as well seem to indicate this started December 2. Turning off all notifications on apps (one by one, as fast as possible in 30-40 seconds until the next restart) seems to have helped many. Others report moving the time back helps this but breaks other functions so this might be a time based bug on iOS 11.1.2 and earlier
The initial analysis is that a local notification where the app sets a daily meditation or daily writing reminder is causing the home screen to “respring” when the time to present the notification arrives or when the processing starts on 2 December.
If you have an App Store app installed that sends local notifications, once you hit December 2, 2017 local time, your iPhone could begin to crash.
It seems prudent to connect to a computer to back up if you can or initiate an iCloud backup now. There is an iOS 11.2 release that may fix this as well if you don’t want to mess with the date (which may break more than just a respring) or toggle notifications on an app by app basis.