  An energy gap develops near quantum critical point of quantum phase
transition in a finite many-body (MB) system, facilitating the ground state
transformation by adiabatic parameter change. In real application scenarios,
however, the efficacy for such a protocol is compromised by the need to balance
finite system life time with adiabaticity, as exemplified in a recent
experiment that prepares three-mode balanced Dicke state near deterministically
[PNAS {\bf 115}, 6381 (2018)]. Instead of tracking the instantaneous ground
state as unanimously required for most adiabatic crossing, this work reports a
faster sweeping policy taking advantage of excited level dynamics. It is
obtained based on deep reinforcement learning (DRL) from a multi-step training
scheme we develop. In the absence of loss, a fidelity $\ge 99\%$ between
prepared and the target Dicke state is achieved over a small fraction of the
adiabatically required time. When loss is included, training is carried out
according to an operational benchmark, the interferometric sensitivity of the
prepared state instead of fidelity, leading to better sensitivity in about half
of the previously reported time. Implemented in a Bose-Einstein condensate of
$\sim 10^4$ $^{87}$Rb atoms, the balanced three-mode Dicke state exhibiting an
improved number squeezing of $13.02\pm0.20$ dB is observed within 766 ms,
highlighting the potential of DRL for quantum dynamics control and quantum
state preparation in interacting MB systems.
