We stabilize an open cavity flow experiment to 1% of its original fluctuation level. For the first time, a multi-modal feedback control is automatically learned for this configuration. The key enabler is automatic in situ optimization of control laws with machine learning augmented by a gradient descent algorithm, named gradient-enriched machine learning control (Cornejo Maceda et al., J. Fluid Mech., vol. 917, 2021, A42, gMLC). The physical interpretation of the feedback mechanism is assisted by a novel cluster-based control law visualization for the flow dynamics and corresponding actuation commands. Starting points of the control experiment are two unforced open cavity benchmark configurations: a narrow-bandwidth regime with a single dominant frequency and a mode-switching regime where two frequencies compete. The flow is forced by a dielectric barrier discharge actuator located at the leading edge and is monitored by a downstream hot-wire sensor over the trailing edge. The feedback law is optimized with respect to the monitored fluctuation level. As reference, the self-oscillations of the mixing layer are mitigated with steady actuation. Then, a feedback controller is optimized with gMLC. As expected, feedback control outperforms steady actuation by achieving a better amplitude reduction with approximately 1% of the actuation energy required for similarly effective steady forcing. Intriguingly, optimized laws learned for one regime perform well for the other untested regime as well. The proposed control strategy can be expected to be applicable for many other shear flow experiments.