if you terminate the lease based on this student status, you could be in trouble according the the fair housing act. Even though the student status is not a protected class, but it could be used to age and marital status which are protected class.
In NY, you cannot pump the rent more than 3%, you also have to check your lease agreement for further action.
Basic rules here, you can terminate the lease based on behaviour, but it's against the law if you terminate based on the status or classes.