There are many strains of Caulerpa, I have a really nasty one that is challenging my patience. I found mine here
http://saltcorner.com/sections/guest/algaepage/algaepage.htm The only drawback is there is a guide to natural predators of all algae found there except Caulerpa. I'm not sure why but plan to try to contact the owners of the site and see if they plan to update it.
Beyond manual removal (which in some cases depending on the algae, you may need to be careful of helping spread it) you can at least look at the other critters they list that naturally prey on some algaes and take a chance with different types of control.
As always you want to keep your water parameters and nutrients in check, but some algaes are so invasive they do seemingly fine feeding from your lighting (like Bryopsis)
I am going to shortly be experimenting with both bryopsis and my strain of caulerpa (either peltata or nummuleria its hard to tell from just 1 pic) with Elysia Crispata (lettuce slug) and will let you know if I make any progress with either algaes and the critters.
You can try a lights out period but usually the time required to kill off the algae is too long for your corals and high light inverts to bear. I only recommend MAX 3 days, usually 2 does the job if you're looking to knock out something like cyano.
I wish I had more help to offer

Just get your gardening gloves ready for a weekly algae harvest. Now that I think about it I forgot to throw away the cup i took out last night. Hope it doesnt make the house smell!