If you have a lease, your tenant is responsible for the rent until the end of the lease. If he/she wants out a month early, you can agree to try and find someone to rent it starting 2/1 but, they're responsible for the rent until the new person moves in or the lease is up (whichever comes first). I believe in working with my tenants and being as flexible as possible but, an agreement is an agreement. Good luck.
As far as rental increases, I do them every year and try to keep them small rather than a big increase every few years or, gasp, no increase at all (assuming area comps support an increase). The tenants expect it so, it should be no surprise.