The control requirements for modern liquid rocket engines are increasing due to demands such as reusability, wide-range throttling, and multiple restart capability. These demands lead to highly nonlinear dynamics, strong subsystem coupling, strict safety constraints, and the need for fast control decisions on resource-constrained onboard hardware. Despite their ability to handle nonlinear systems, neural networks are rarely applied to safety-critical control tasks, particularly in rocket engine control, due to concerns regarding robustness and certification. This work presents a reinforcement learning (RL)–based control strategy for the LUMEN (Liquid Upper-stage demonstrator Engine) engine. Since reinforcement learning relies on trial-and-error interactions and experimental data for rocket engines is prohibitively expensive, the controller is trained entirely in a high-fidelity simulation environment that captures the engine’s nonlinear dynamics, actuator limitations, and operational constraints. While previous studies have demonstrated RL-based control of rocket engine simulations, they were limited to tracking predefined operating points and fixed transition ramps. In contrast, the proposed controller can autonomously transition between arbitrary set points within the admissible operating space of the LUMEN engine, without relying on predefined trajectories or scheduling logic. The learned policy directly maps the current engine state and target conditions to control actions, enabling flexible operation across the full envelope. Simulation results demonstrate stable and accurate set-point tracking while respecting operational constraints. Overall, this work shows that reinforcement learning enables flexible and autonomous control of nonlinear and constrained rocket engines, representing an important step toward intelligent control architectures for future reusable launch systems.