Make sure you have the unattended-upgrades package installed, then configure the following options in /etc/apt/apt.conf.d/50unattended-upgrades:
// Automatically upgrade packages from these (origin:archive) pairs
Unattended-Upgrade::Allowed-Origins {
"Ubuntu:precise";
"Ubuntu:precise-security";
"Ubuntu:precise-updates";
"Ubuntu:precise-backports";
"Canonical:precise";
};
// This option allows you to control if on a unclean dpkg exit
// unattended-upgrades will automatically run
// dpkg --force-confold --configure -a
// The default is true, to ensure updates keep getting installed
Unattended-Upgrade::AutoFixInterruptedDpkg "true";
// Split the upgrade into the smallest possible chunks so that
// they can be interrupted with SIGUSR1. This makes the upgrade
// a bit slower but it has the benefit that shutdown while a upgrade
// is running is possible (with a small delay)
Unattended-Upgrade::MinimalSteps "true";
// Install all unattended-upgrades when the machine is shuting down
// instead of doing it in the background while the machine is running
// This will (obviously) make shutdown slower
Unattended-Upgrade::InstallOnShutdown "true";
// Do automatic removal of new unused dependencies after the upgrade
// (equivalent to apt-get autoremove)
Unattended-Upgrade::Remove-Unused-Dependencies "true";
Inside the Unattended-Upgrade::Allowed-Origins block, replace precise with your actual Ubuntu codename (output of lsb_release -cs).