at any rate - Phrases/Idioms
The American Heritage® Dictionary of Idioms by Christine Ammer. Copyright © 2003, 1997 by The Christine Ammer 1992 Trust. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.
In any event, whatever the case may be; also, at least. For example, At any rate, I promise to be there even if I'm a little late, or It may not pay well, but at any rate it's a job. [Early 1600s] Also see in any case.