  We present a new theoretical model and numerical optimization of double Bragg
diffraction (DBD), a widely used technique in atom interferometry. We derive an
effective two-level-system Hamiltonian based on the Magnus expansion in the
so-called "quasi-Bragg regime", where most Bragg-pulse atom interferometers
operate. Furthermore, we extend the theory to a five-level description to
account for Doppler detuning. Using these derived effective Hamiltonians, we
investigate the impacts of AC-Stark shift and polarization errors on the double
Bragg beam-splitter, along with their mitigations through detuning control.
Notably, we design a linear detuning sweep that demonstrates robust efficiency
exceeding 99.5% against polarization errors up to 8.5%. Moreover, we develop an
artificial intelligence-aided optimal detuning control protocol, showcasing
enhanced robustness against both polarization errors and Doppler effects. This
protocol achieves an average efficiency of 99.92% for samples with a finite
momentum width of 0.05$\hbar k_L$ within an extended polarization error range
of up to 10%.
