I just downloaded Okular from Ubuntu Software.
I see that I downloaded Okular version 1.1.3. I see on the website that there is a version that is newer than the one I got.
Can this be auto updated ?

I'm running kde neon which runs on ubuntu 16.04 LTS and I have okular 1.2.2 aka 17.08.2 maybe okular being a kubuntu/kde product allows a newer version of okular? Ubuntu uses Document Viewer to view pdf files, not okular. Okular is made available in the ubuntu repositories as an option.

https://repology.org/metapackage/okular/versions
This page lists the versions of okular are made available for different desktops. Ubuntu 17.10 comes with okular 17.04.03 but I don't know what that translates to - most likely 1.1.3?

Obviously ubuntu chose that version for a reason. According to the release news, no features to speak of were added in 1.2.x. Version 1.1.x however did add features so you should be up to date as far as features go. As far as auto-update, that's up to ubuntu.

A bit late, but in general, if you use a certain distribution, the distribution decides the policy of updates. So you should choose a distribution that fits your idea of how frequently and how big the updates should be.