look for vacant units in your building (if you're in an apartment) and see if you can negotiate a lower rate with your landlord based on the price of the units that are currently up for rent. if you're not in an apartment, you might be able to do the same thing with houses in your area
You could incentivize them by offering to extend your lease early, if you can lock in a lower rent.
You should at least try to lower your rent. The worst thing that can happen is your rent doesn't change. You might get a discount, which you certainly won't get if you don't ask.
Unfortunately, I can't do that because I will be moving for a new job when the lease is up. Agree that its worth an ask, but don't think it's particularly likely anything will come of it.