  Adaptive data collection and analysis, where data are being fed back to
update the measurement settings, can greatly increase speed, precision, and
reliability of the characterization of quantum systems. However, decoherence
tends to make adaptive characterization difficult. As an example, we consider
two coupled discrete quantum systems. When one of the systems can be controlled
and measured, the standard method to characterize another, with an unknown
frequency $\omega_{\rm r}$, is swap spectroscopy. Here, adapting measurements
can provide estimates whose error decreases exponentially in the number of
measurement shots rather than as a power law in conventional swap spectroscopy.
However, when the decoherence time is so short that an excitation oscillating
between the two systems can only undergo less than a few tens of vacuum Rabi
oscillations, this approach can be marred by a severe limit on accuracy unless
carefully designed. We adopt machine learning techniques to search for
efficient policies for the characterization of decohering quantum systems. We
find, for instance, that when the system undergoes more than 2 Rabi
oscillations during its relaxation time $T_1$, $O(10^3)$ measurement shots are
sufficient to reduce the squared error of the Bayesian initial prior of the
unknown frequency $\omega_{\rm r}$ by a factor $O(10^4)$ or larger. We also
develop policies optimized for extreme initial parameter uncertainty and for
the presence of imperfections in the readout.
