Unconditional well-posendness for the fourth order nonlinear Schrodinger type equations on the torus

We prove the unconditional well-posedness for the fourth order nonlinear Schrodinger type equations in H^s($\mathbb{T}$) when s \geq 1, which includes the non-integrable case. This regularity threshold is optimal because the nonlinear terms cannot be defined in the space-time distribution framework for s<1. The main idea is to employ the normal form reduction and a kind of cancellation property to deal with derivative losses.