Speech recognition is a sequence prediction problem. Besides employing various deep learning approaches for frame-level classification, sequence-level discriminative training has been proved to be indispensable to achieve the state-of-the-art performance in large vocabulary continuous speech recognition (LVCSR). However, keyword spotting (KWS), as one of the most common speech recognition tasks, almost only benefits from frame-level deep learning due to the difficulty of getting competing sequence hypotheses. The few studies on sequence discriminative training for KWS are limited for fixed vocabulary or LVCSR based methods and have not been compared to the state-of-the-art deep learning based KWS approaches. In this paper, a sequence discriminative training framework is proposed for both fixed vocabulary and unrestricted acoustic KWS. Sequence discriminative training for both sequence-level generative and discriminative models are systematically investigated. By introducing word-independent phone lattices or non-keyword blank symbols to construct competing hypotheses, feasible and efficient sequence discriminative training approaches are proposed for acoustic KWS. Experiments showed that the proposed approaches obtained consistent and significant improvement in both fixed vocabulary and unrestricted KWS tasks, compared to previous frame-level deep learning based acoustic KWS methods.