The Oreo update has gone smoothly for most Pixel owners, but it hasn't gone perfectly for everyone. Some Pixel owners have been plagued by reboot issues since that update, and the cause has been difficult to pin down. According to Google, the OTAs rolling out today on Pixel devices will stop the reboots, which have a few distinct causes.
Probably the most common reboot issue in Oreo is related to picture-in-picture with YouTube. Sometimes the Pixel just reboots when launching PiP mode. This issue was known internally to Google, and is fixed in the October patch. The other problem was a bit more elusive. Affected devices could go for days without any issues, and then there would be multiple reboots in a few minutes. This one is probably related to what Google is calling a file descriptor (fd) leak, which is fixed in the update. Here's the Googler reply on that thread.
Oct 2017 Pixel update has been released.
Images are posted here https://developers.google.com/android/otafor those interested in using "adb sideload" to install. You can also try using "Settings > System > System update" and "Check for update" to see if it is available to you.
I believe this will address the YouTube PIP issue and the fd leak b/63784898 that I believe is associated with this issue.
Artem and others, would appreciate confirmation if this fixes your issues and if not I'd appreciate further bugreports on the new builds since logging has been improved.
There are four separate threads in the tracker for spontaneous reboots on Oreo (1, 2, 3, 4). The first is marked as "won't fix" in the tracker, because it's likely related to a hardware issue. The other three are still unsolved, but someone is apparently assigned to look at the problem.
The new OTAs are available now. You can get the file and sideload on your device, or head to the update menu and try to download it the old-fashioned way. Pixels are supposed to be able to pull the latest update when you hit the button, but it's not showing up for me yet.