Recent research has shown the potential of Nash Learning via Human Feedback for large language model alignment by incorporating the notion of a preference model in a minimax game setup.We take this idea further by casting the alignment as a mirror descent algorithm against the adaptive feedback of an improved opponent, thereby removing the need for learning a preference model or the existence of an annotated dataset altogether.The resulting algorithm, which we refer to as Language Alignment via Nash-learning and Adaptive feedback (LANA), is capable of self-alignment without the need for a human-annotated preference dataset. We support this statement with various experiments and mathematical discussion.