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While spin qubits based on gate-defined quantum dots have demonstrated very favorable properties for quantum computing, one remaining hurdle is the need to tune each of them into a good operating regime by adjusting the voltages applied to electrostatic gates. The automation of these tuning procedures is a necessary requirement for the operation of a quantum processor based on gate-defined quantum dots, which is yet to be fully addressed. We present an algorithm for the automated fine-tuning of quantum dots and demonstrate its performance on a semiconductor singlet-triplet qubit in GaAs. The algorithm employs a Kalman filter based on Bayesian statistics to estimate the gradients of the target parameters as a function of gate voltages, thus learning the system response. The algorithm's design is focused on the reduction of the number of required measurements. We experimentally demonstrate the ability to change the operation regime of the qubit within 3–5 iterations, corresponding to 10–15 min of lab-time. [ABSTRACT FROM AUTHOR]