During the off-road path following of a wheeled mobile robot in presence of poor grip conditions, the longitudinal velocity should be limited in order to maintain safe navigation with limited tracking errors, while at the same time being high enough to minimize travel time. Thus, this paper presents a new approach of online speed fluctuation, capable of limiting the lateral error below a given threshold, while maximizing the longitudinal velocity. This is accomplished using a neural network trained with a reinforcement learning method. This speed modulation is done side-by-side with an existing model-based predictive steering control, using a state estimator and dynamic observers. Simulated and experimental results show a decrease in tracking error, while maintaining a consistent travel time when compared to a classical constant speed method and to a kinematic speed fluctuation method.