Is it okay if research problem is vague in the initial phase of research?
In my opinion this is the definition of "research" everything else is "development". Of course, from "devlopment", serious research questions may be derived. 

In my personal opinion, a PhD work whose proposed result is known from the beginning is worthless.

It's a different story if the problem is too large for one person or maybe not solvable at all - then it needs to be re-adjusted based on the experience made so far. But this process can / shall be part of the PhD!