Many machine learning algorithms minimize a regularized risk. It is well known that stochastic optimization algorithms are both theoretically and practically well motivated for regularized risk minimization. Unfortunately, stochastic optimization is not easy to parallelize. In this talk, we take a radically new approach and show that working with the saddle-point problem that arises out of the Lagrangian has a very specific computational graph structure which can be exploited to allow for a natural partitioning of the parameters across multiple processors. This allows us to derive a new parallel stochastic optimization algorithm for regularized risk minimization. Joint work with: Inderjit Dhillon, Cho-Jui Hsieh, Shihao Ji, Shin Matsushima, Parameshwaran Raman, Hsiang-Fu Yu, and Hyokun Yun.