The convergence of the initiator method to the exact FCI limit with the number of walkers can be further accelerated with the help of the adaptive shift method. The initiator bias is mainly attributed to the missing back-spawns onto the non-initiators resulting from their underpopulated local Hilbert space. This bias is ameliorated in the adaptive shift method by reducing the shift of non-initiators and thus boosting their lifetime to compensate for the missing back-spawns. In the adaptive shift method, each determinant D i gets its own local shift S i as a fraction of the total global shift S