This document proposes MORLOT (Many-Objective Reinforcement Learning for Online Testing) to address challenges in online testing of DNN-enabled systems. MORLOT leverages many-objective search and reinforcement learning to choose test actions. It was evaluated on the Transfuser autonomous driving system in the CARLA simulator using 6 safety requirements. MORLOT was significantly more effective and efficient at finding safety violations than random search or other many-objective approaches, achieving a higher average test effectiveness for any given test budget.