A hearing aid includes a forward path including a) an input transducer proving an electric input signal, b) a hearing aid processor, and c) an output transducer. The hearing aid further includes d) a feedback control system having d1) a feedback path estimator including an adaptive filter configured to provide an estimate of a current feedback path from the output transducer to at least one input transducer, the feedback path estimator being controllable via a feedback estimation control input, and d2) a combination unit in the forward path configured to subtract the estimate (v′) of the current feedback path signal (v) from a signal of the forward path (y) to provide a feedback corrected signal (e), and e) a detector for providing the feedback estimation control input in dependence of an offset control signal indicative of an offset in the electric input signal or a signal originating therefrom.