  We present methods for efficient characterization of an optical coherent
state $|\alpha\rangle$. We choose measurement settings adaptively and
stochastically, based on data while it is collected. Our algorithm divides the
estimation into two distinct steps: (i) before the first detection of a vacuum
state, the probability of choosing a measurement setting is proportional to
detecting vacuum with the setting, which makes using too similar measurement
settings twice unlikely; and (ii) after the first detection of vacuum, we focus
measurements in the region where vacuum is most likely to be detected. In step
(i) [(ii)] the detection of vacuum (a photon) has a significantly larger effect
on the shape of the posterior probability distribution of $\alpha$. Compared to
nonadaptive schemes, our method makes the number of measurement shots required
to achieve a certain level of accuracy smaller approximately by a factor
proportional to the area describing the initial uncertainty of $\alpha$ in
phase space. While this algorithm is not directly robust against readout
errors, we make it such by introducing repeated measurements in step (i).
