In this work, we derive the non-equilibrium Fermi's golden rule (NE-FGR) theory for the polariton relaxation processes and simulate the polariton relaxation dynamics via quantum master equation approaches. The application of such a perturbative population dynamics method (i.e. the NE-FGR rate theory) implies that the off-diagonal elements of the Hamiltonian are treated as a perturbation. For the system DOF, the polariton basis is used such that the system Hamiltonian is diagonalized. In this case, the exciton-phonon couplings become the perturbation.