We experimentally demonstrate the application of a double deep Q-learning network algorithm (DDQN) for design of a self-starting fiber mode-locked laser. In contrast to the static optimization of a system design, the DDQN reinforcement algorithm is capable of learning the strategy of dynamic adjustment of the cavity parameters. Here, we apply the DDQN algorithm for stable soliton generation in a fiber laser cavity exploiting a nonlinear polarization evolution mechanism. The algorithm learns the hysteresis phenomena that manifest themselves as different pumping-power thresholds for mode-locked regimes for diverse trajectories of adjusting optical pumping.