We propose an idea for line search algorithms in multi-task learning. The idea is to use latent representation space instead of parameter space for finding step size. We examined this idea with backtracking line search. We compare this fast backtracking algorithm with classical backtracking and gradient methods with a constant learning rate on MNIST, CIFAR-10, Cityscapes tasks. The systematic empirical study showed that the proposed method leads to more accurate and fast solution than the traditional backtracking approach and keep competitive computational time and performance compared to the constant learning rate method.