This might sound hypocritical since I met my wife at a previous job, but whether the company forbids interoffice dating or not, I don't think it's a good idea.
I work with a lot of younger people - for most of them, it's their first "real" job - and the aftermath of the (mostly) inevitable breakups causes a lot of problems on the job.
Guys in their mid-20s with good incomes are hitting on girls right out of school, the girls usually fall like mad and after a couple months the guys move on to another one. The girl ends up crying all day, calling and emailing her friends to discuss it, and it ends up hurting her performance review. Then Mary says she doesn't want to work with Bill, and who looks bad? It's ain't Bill!
If it's the guy who got dumped, he gets agitated when he has to interact with the "ex", and his work reputation suffers because he has trouble working with certain people. Usually girls at work form friendships and not only does he not want to be around the "ex", but he doesn't like to be around her work friends either.
No matter how discreet you are, people are going to find out. If the company doesn't allow it, they may not say anything to you, but it will be held against you anyway. You'll just never know it.