Is there any way to force sudo to not log actions from a specific user?

All of the servers in my network are running a Zabbix agent for monitoring, and some of the additional items I've added to them require the use of sudo to execute. Normally this isn't that bad, but for one in particular, this results in about 75 lines every minute in the journal relating to it's usual data gathering.

Is there any way to specifically tell sudo to not log anything for a particular user?

I tried adding

Defaults:zabbix logfile=/dev/null

to my sudoers file, which stopped the session opened and session closed log lines, but isn't stopping this mess:

sudo[12424]:   zabbix : TTY=unknown ; PWD=/ ; USER=root ; COMMAND=...
sudo[12433]:   zabbix : TTY=unknown ; PWD=/ ; USER=root ; COMMAND=...
sudo[12435]:   zabbix : TTY=unknown ; PWD=/ ; USER=root ; COMMAND=...
sudo[12437]:   zabbix : TTY=unknown ; PWD=/ ; USER=root ; COMMAND=...
sudo[12449]:   zabbix : TTY=unknown ; PWD=/ ; USER=root ; COMMAND=...
sudo[12459]:   zabbix : TTY=unknown ; PWD=/ ; USER=root ; COMMAND=...
sudo[12465]:   zabbix : TTY=unknown ; PWD=/ ; USER=root ; COMMAND=...
sudo[12467]:   zabbix : TTY=unknown ; PWD=/ ; USER=root ; COMMAND=...