Audio Research Ref 3 set display off/on.

Sorry, I will mention the obvious answer which is of course to give ARC a call.  But it does make sense that the display would default to being on after each power up.

I would assume most people would normally want to defeat the lights when listening at night.   If you are like me, there is always the chance that I could accidentally not realize it is on when display lights are defeated and keep it running a long time before noticing.

The problem is that this display produces an audible noise, bzzzzz noise.I had Cary Audio SLP-03 and it remembered display setting on OFF.

I am curious are there any tweaks/fixes which allow to remember display setting when amp is OFF? 

My Ref 3 always powers up with the display on and always has.  It's the display buzzing that is not normal.  
For kicks try setting the Ref 3 to mono and use the balance control.  Now THAT is a messed up situation.