We study a stochastic and distributed algorithm for nonconvex problems whose objective consists of a sum of N nonconvex Li/N-smooth functions, plus a non-smooth regularizer. The proposed NonconvEx primal-dual SpliTTing (NESTT) algorithm splits the problem into 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 ϵ-stationary solution using O((ΣNi=1 √Li/N)2/ϵ) gradient evaluations, which can be up to O(N) times better than the (proximal) gradient descent methods. It also achieves Q-linear convergence rate for nonconvex l1 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.
|Original language||English (US)|
|Number of pages||9|
|Journal||Advances in Neural Information Processing Systems|
|State||Published - Jan 1 2016|
|Event||30th Annual Conference on Neural Information Processing Systems, NIPS 2016 - Barcelona, Spain|
Duration: Dec 5 2016 → Dec 10 2016