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We introduce a novel approach for sequence decoding, Discriminative Adversarial Search (DAS), which has the desirable properties of alleviating the effects of exposure bias without requiring external metrics. Inspired by Generative Adversarial Networks (GANs), wherein a discriminator is used to improve the generator, our method differs from GANs in that the generator parameters are not updated at training time and the discriminator is only used to drive sequence generation at inference time. We investigate the effectiveness of the proposed approach on the task of Abstractive Summarization: the results obtained show that a naive application of DAS improves over the state-of-the-art methods, with further gains obtained via discriminator retraining. Moreover, we show how DAS can be effective for cross-domain adaptation. Finally, all results reported are obtained without additional rule-based filtering strategies, commonly used by the best performing systems available: this indicates that DAS can effectively be deployed without relying on post-hoc modifications of the generated outputs.