Doubly Stochastic Primal-Dual Coordinate Method for Empirical Risk Minimization

We proposed a doubly stochastic primal-dual coordinate optimization algorithm for regularized empirical risk minimization that can be formulated as a saddle-point problem using convex conjugate functions. Different from the existing coordinate methods, the proposed method randomly samples both primal and dual coordinates to update solutions. The convergence of our method is established in both the solution's distance to optimality and the primal-dual objective gap. When applied to the data matrix factorized as a product of two smaller matrices, we show that the proposed method has a lower overall complexity than other coordinate methods, especially, when data size is large. Furthermore, we also generalize the method for convex saddle-point problem with a block-wise decomposable structure and give a lower bound for the iteration complexity of a family of primal-dual coordinate method for solving such a problem. This is joint work with Qihang Lin (UIowa) and Tianbao Yang (UIowa).

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I really appreciate MSR publishing so many useful talks. But they really should focus more on slides as opposed to speakers facial expressions...