Abstract
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) |
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Pages (from-to) | 3215-3223 |
Number of pages | 9 |
Journal | Advances in Neural Information Processing Systems |
State | Published - 2016 |
Externally published | Yes |
Event | 30th Annual Conference on Neural Information Processing Systems, NIPS 2016 - Barcelona, Spain Duration: Dec 5 2016 → Dec 10 2016 |
Bibliographical note
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