Davood Hajinezhad from Dr. Mingyi Hong’s group will be presenting this week on “A Nonconvex Primal-Dual Splitting Method for Distributed and Stochastic Optimization”. Details of the talk are as given below:
Abstract: We study a stochastic and distributed algorithm for nonconvex problems whose objective consists of a sum of $latex N$ nonconvex $latex L_i/N$-smooth functions, plus a nonsmooth regularizer. The proposed NonconvEx primal-dual SpliTTing (NESTT) algorithm splits the problem into $latex N$ subproblems, and utilizes an augmented Lagrangian based primal-dual scheme to solve it in a distributed and stochastic manner. With a special non-uniform sampling, a version of NESTT achieves $latex \epsilon$-stationary solution using $latex O((\sum_{i=1}^N\sqrt{L_i/N})^2/\epsilon)$ gradient evaluations, which can be up to $latex O(N)$ times better than the (proximal) gradient descent methods. It also achieves Q-linear convergence rate for nonconvex $latex \ell_1$ penalized quadratic problems with polyhedral constraints. Further, we reveal a fundamental connection between primal-dual based methods and a few primal only methods such as IAG/SAG/SAGA.