  Unsupervised bilingual lexicon induction naturally exhibits duality, which
results from symmetry in back-translation. For example, EN-IT and IT-EN
induction can be mutually primal and dual problems. Current state-of-the-art
methods, however, consider the two tasks independently. In this paper, we
propose to train primal and dual models jointly, using regularizers to
encourage consistency in back translation cycles. Experiments across 6 language
pairs show that the proposed method significantly outperforms competitive
baselines, obtaining the best-published results on a standard benchmark.
