  Reinforcement learning is a general methodology of adaptive optimal control
that has attracted much attention in various fields ranging from video game
industry to robot manipulators. Despite its remarkable performance
demonstrations, plain reinforcement learning controllers do not guarantee
stability which compromises their applicability in industry. To provide such
guarantees, measures have to be taken. This gives rise to what could generally
be called stabilizing reinforcement learning. Concrete approaches range from
employment of human overseers to filter out unsafe actions to formally verified
shields and fusion with classical stabilizing controllers. A line of attack
that utilizes elements of adaptive control has become fairly popular in the
recent years. In this note, we critically address such an approach in a fairly
general actor-critic setup for nonlinear time-continuous environments. The
actor network utilizes a so-called robustifying term that is supposed to
compensate for the neural network errors. The corresponding stability analysis
is based on the value function itself. We indicate a problem in such a
stability analysis and provide a counterexample to the overall control scheme.
Implications for such a line of attack in stabilizing reinforcement learning
are discussed. Furthermore, unfortunately the said problem possess no fix
without a substantial reconsideration of the whole approach. As a positive
message, we derive a stochastic critic neural network weight convergence
analysis provided that the environment was stabilized.
