Abstract: In simultaneous speech translation (SimulST), effective policies that determine when to write partial translations are crucial to reach high output quality with low latency. Towards this objective, we propose EDAtt (Encoder-Decoder Attention), an adaptive policy that exploits the attention patterns between audio source and target textual translation to guide an offline-trained ST model during simultaneous inference. EDAtt exploits the attention scores modeling the audio-translation relation to decide whether to emit a partial hypothesis or wait for more audio input. This is done under the assumption that, if attention is focused towards the most recently received speech segments, the information they provide can be insufficient to generate the hypothesis (indicating that the system has to wait for additional audio input). Results on en->{de, es} show that EDAtt yields better results compared to the SimulST state of the art, with gains respectively up to 7 and 4 BLEU points for the two languages, and with a reduction in computational-aware latency up to 1.4s and 0.7s compared to existing SimulST policies applied to offline-trained models.