  To find the path that minimizes the time to navigate between two given points
in a fluid flow is known as Zermelo's problem. Here, we investigate it by using
a Reinforcement Learning (RL) approach for the case of a vessel which has a
slip velocity with fixed intensity, Vs , but variable direction and navigating
in a 2D turbulent sea. We show that an Actor-Critic RL algorithm is able to
find quasi-optimal solutions for both time-independent and chaotically evolving
flow configurations. For the frozen case, we also compared the results with
strategies obtained analytically from continuous Optimal Navigation (ON)
protocols. We show that for our application, ON solutions are unstable for the
typical duration of the navigation process, and are therefore not useful in
practice. On the other hand, RL solutions are much more robust with respect to
small changes in the initial conditions and to external noise, even when V s is
much smaller than the maximum flow velocity. Furthermore, we show how the RL
approach is able to take advantage of the flow properties in order to reach the
target, especially when the steering speed is small.
