  We formulate the theory for steering an active particle with optimal travel
time between two locations and apply it to the Mexican hat potential without
brim. For small heights the particle can cross the potential barrier, while for
large heights it has to move around it. Thermal fluctuations in the orientation
strongly affect the path over the barrier. Then we consider a smart active
particle and apply reinforcement learning. We show how the active particle
learns in repeating episodes to move optimally. The optimal steering is stored
in the optimized action-value function, which is able to rectify thermal
fluctuations.
