A319 Captain reported gate agent closed and reopened the main aircraft door. Escape slide did not deploy.

Narrative

While I was conducting my preflight briefing; the gate agent came into the cockpit; handed the release to the first officer without saying anything; and left.Per the purser's comments to me; the gate agent also didn't ask the purser if she was ready to close the main cabin door. The gate agent shut the main cabin door and then reopened it a few seconds later (perhaps conducting training). This concerned my purser because it could have resulted in an ISD if she had armed the door right after the gate agent closed it. The first indication I had that the Main Cabin Door (MCD) had been closed was when I saw the jet bridge pulling away. We pushed 4 minutes early; so there was no need to rush.