The growing amount of high dimensional data in different machine learning applications requires more efficient and scalable optimization algorithms. In this work, we consider combining two techniques, parallelism and Nesterov’s acceleration, to design faster algorithms for L1-regularized loss. We first simplify BOOM , a variant of gradient descent, and study it in a unified framework, which allows us to not only propose a refined measurement of sparsity to improve BOOM, but also show that BOOM is provably slower than FISTA . Moving on to parallel coordinate descent methods, we then propose an efficient accelerated version of Shotgun , improving the convergence rate from O(1/t) to O(1/t). Our algorithm enjoys a concise form and analysis compared to previous work, and also allows one to study several connected work in a unified way.