Abstract: Reinforcement Learning (RL) is a powerful framework to address the discrepancy between loss functions used during training and the final evaluation metrics to be used at test time. When applied to neural Machine Translation (MT), it minimises the mismatch between the cross-entropy loss and non-differentiable evaluation metrics like BLEU. However, the suitability of these metrics as reward function at training time is questionable: they tend to be sparse and biased towards the specific words used in the reference texts. We propose to address this problem by making models less reliant on such metrics in two ways: (a) with an entropy-regularised RL method that does not only maximise a reward function but also explore the action space to avoid peaky distributions; (b) with a novel RL method that explores a dynamic unsupervised reward function to balance between exploration and exploitation. We base our proposals on the Soft Actor-Critic (SAC) framework, adapting the off-policy maximum entropy model for language generation applications such as MT. We demonstrate that SAC with BLEU reward tends to overfit less to the training data and performs better on out-of-domain data. We also show that our dynamic unsupervised reward can lead to better translation of ambiguous words.