  In the workflow of Full-Waveform Inversion (FWI), we often tune the
parameters of the inversion to help us avoid cycle skipping and obtain high
resolution models. For example, typically start by using objective functions
that avoid cycle skipping, like tomographic and image based or using only low
frequency, and then later, we utilize the least squares misfit to admit high
resolution information. We also may perform an isotropic (acoustic) inversion
to first update the velocity model and then switch to multi-parameter
anisotropic (elastic) inversions to fully recover the complex physics. Such
hierarchical approaches are common in FWI, and they often depend on our manual
intervention based on many factors, and of course, results depend on
experience. However, with the large data size often involved in the inversion
and the complexity of the process, making optimal choices is difficult even for
an experienced practitioner. Thus, as an example, and within the framework of
reinforcement learning, we utilize a deep-Q network (DQN) to learn an optimal
policy to determine the proper timing to switch between different misfit
functions. Specifically, we train the state-action value function (Q) to
predict when to use the conventional L2-norm misfit function or the more
advanced optimal-transport matching-filter (OTMF) misfit to mitigate the
cycle-skipping and obtain high resolution, as well as improve convergence. We
use a simple while demonstrative shifted-signal inversion examples to
demonstrate the basic principles of the proposed method.
