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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. 2021, gMLC). gMLC is shown to learn one order of magnitude faster than MLC (Duriez et al. 2017, MLC). The physical interpretation of the feedback mechanism is assisted by a novel cluster-based control law visualization for flow dynamics and corresponding actuation commands. Starting point 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 feedback control commands the DBD actuator located at the leading edge. The flow 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 both, a better amplitude reduction and a significantly smaller actuation power, about about 1% of the actuation energy required for similarly effective steady forcing. Intriguingly, optimized laws learned for one regime performs well for the other untested regime as well. The proposed control strategy can be expected to be applicable for many other shear flow experiments.