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Deep learning has been recently introduced for efficient acoustic howling suppression (AHS). However, the recurrent nature of howling creates a mismatch between offline training and streaming inference, limiting the quality of enhanced speech. To address this limitation, we propose a hybrid method that combines a Kalman filter with a self-attentive recurrent neural network (SARNN) to leverage their respective advantages for robust AHS. During offline training, a pre-processed signal obtained from the Kalman filter and an ideal microphone signal generated via teacher-forced training strategy are used to train the deep neural network (DNN). During streaming inference, the DNN's parameters are fixed while its output serves as a reference signal for updating the Kalman filter. Evaluation in both offline and streaming inference scenarios using simulated and real-recorded data shows that the proposed method efficiently suppresses howling and consistently outperforms baselines.