  Recently proposed quantum-chaotic sensors achieve quantum enhancements in
measurement precision by applying nonlinear control pulses to the dynamics of
the quantum sensor while using classical initial states that are easy to
prepare. Here, we use the cross-entropy method of reinforcement learning to
optimize the strength and position of control pulses. Compared to the
quantum-chaotic sensors with periodic control pulses in the presence of
superradiant damping, we find that decoherence can be fought even better and
measurement precision can be enhanced further by optimizing the control. In
some examples, we find enhancements in sensitivity by more than an order of
magnitude. By visualizing the evolution of the quantum state, the mechanism
exploited by the reinforcement learning method is identified as a kind of
spin-squeezing strategy that is adapted to the superradiant damping.
