The proposed approach consists in corrupting the training targets with a noise derived from the task reward while doing maximum likelihood training. This simple but specific smoothing of the target distribution allows to significantly boost the performance of neural structured output prediction as showcased on TIMIT phone and translation tasks. The link between this approach and RL-based expected reward maximization is also made clear by the paper, Prior work has chosen either maximum likelihood learning, which is relatively tractable but assumes a log likelihood loss, or reinforcement learning, which can be performed for a task-specific loss function but requires sampling many predictions to estimate gradients. The proposed objective bridges the gap with "reward-augmented maximum likelihood," which is similar to maximum likelihood but estimates the expected loss with samples that are drawn in proportion to their distance from the ground truth. Empirical results show good improvements with LSTM-based predictors on speech recognition and machine translation benchmarks relative to maximum likelihood training. This work is inspired by recent advancement in reinforcement learning and likelihood learning. The authors suggest to learn parameters so as to minimize the KL divergence between CRFs and a probability model that is proportional to the reward function (which the authors call payoff distribution, see Equation 4). The authors suggest an optimization algorithm for the KL-divergence minimization that depends on sampling from the payoff distribution. Current methods to learn a model for structured prediction include max margin optimisation and reinforcement learning. However, the max margin approach only optimises a bound on the true reward, and requires loss augmented inference to obtain gradients, which can be expensive. On the other hand, reinforcement learning does not make use of available supervision, and can therefore struggle when the reward is sparse, and furthermore the gradients can have high variance. The paper proposes a novel approach to learning for problems that involve structured prediction. They relate their approach to simple maximum likelihood (ML) learning and reinforcement learning (RL): ML optimises the KL divergence of a delta distribution relative to the model distribution, and RL optimises the KL divergence of the model distribution relative to the exponentiated reward distribution. They propose reward-augmented maximum likelihood learning, which optimises the KL divergence of the exponentiated reward distribution relative to the model distribution. Compared to RL, the arguments of the KL divergence are swapped. Compared to ML, the delta distribution is generalised to the exponentiated reward distribution. Training is cheap in RML learning. It is only necessary to sample from the output set according to the exponentiated reward distribution. All experiments are performed in speech recognition and machine translation, where the structure over the output set is defined by the edit distance. An improvement is demonstrated over simple ML.