The module learning with errors (MLWE) problem is one of the most promising candidates for constructing quantum-resistant cryptosystems. In this work, we proposed a framework to automatically adjust the level of parallelism in MLWE-based key exchange protocols on GPUs to maximize the protocol execution efficiencies. We observed that the $N$, the dimension of the grids in the GPUs have significant impacts on both the latencies and throughputs of MLWE key exchange protocols. By properly adjusting the related parameters, in the experiments, we show that performance of MLWE based key exchange protocols can be improved across GPU platforms.