  Quantum control can be employed in quantum metrology to improve the precision
limit for the estimation of unknown parameters. The optimal control, however,
typically depends on the actual values of the parameters and thus needs to be
designed adaptively with the updated estimations of those parameters.
Traditional methods, such as gradient ascent pulse engineering (GRAPE), need to
be rerun for each new set of parameters encountered, making the optimization
costly, especially when many parameters are involved. Here we study the
generalizability of optimal control, namely, optimal controls that can be
systematically updated across a range of parameters with minimal cost. In cases
where control channels can completely reverse the shift in the Hamiltonian due
to a change in parameters, we provide an analytical method which efficiently
generates optimal controls for any parameter starting from an initial optimal
control found by either GRAPE or reinforcement learning. When the control
channels are restricted, the analytical scheme is invalid, but reinforcement
learning still retains a level of generalizability, albeit in a narrower range.
In cases where the shift in the Hamiltonian is impossible to decompose to
available control channels, no generalizability is found for either the
reinforcement learning or the analytical scheme. We argue that the
generalization of reinforcement learning is through a mechanism similar to the
analytical scheme. Our results provide insights into when and how the optimal
control in multiparameter quantum metrology can be generalized, thereby
facilitating efficient implementation of optimal quantum estimation of multiple
parameters, particularly for an ensemble of systems with ranges of parameters.
