Recent studies on multi-contrast MRI reconstruction have demonstrated the potential of further accelerating MRI acquisition by exploiting correlation between contrasts. Most of the state-of-the-art approaches have achieved improvement through the development of network architectures for fixed under-sampling patterns, without considering inter-contrast correlation in the under-sampling pattern design. On the other hand, sampling pattern learning methods have shown better reconstruction performance than those with fixed under-sampling patterns. However, most under-sampling pattern learning algorithms are designed for single contrast MRI without exploiting complementary information between contrasts. To this end, we propose a framework to optimize the under-sampling pattern of a target MRI contrast which complements the acquired fully-sampled reference contrast. Specifically, a novel image synthesis network is introduced to extract the redundant information contained in the reference contrast, which is exploited in the subsequent joint pattern optimization and reconstruction network. We have demonstrated superior performance of our learned under-sampling patterns on both public and in-house datasets, compared to the commonly used under-sampling patterns and state-of-the-art methods that jointly optimize the reconstruction network and the under-sampling patterns, up to 8-fold under-sampling factor.