Stabilized SVRG: Simple Variance Reduction for Nonconvex Optimization
Variance reduction techniques like SVRG provide simple and fast algorithms for optimizing a convex finite-sum objective. For nonconvex objectives, these techniques can also find a first-order stationary point (with small gradient). However, in nonconvex optimization it is often crucial to find a sec...
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| Main Authors: | , , , |
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| Format: | text |
| Language: | English |
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Institutional Knowledge at Singapore Management University
2019
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| Online Access: | https://ink.library.smu.edu.sg/sis_research/8677 https://ink.library.smu.edu.sg/context/sis_research/article/9680/viewcontent/COLT19_stabilizedsvrg.pdf |
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| Institution: | Singapore Management University |
| Language: | English |
| Summary: | Variance reduction techniques like SVRG provide simple and fast algorithms for optimizing a convex finite-sum objective. For nonconvex objectives, these techniques can also find a first-order stationary point (with small gradient). However, in nonconvex optimization it is often crucial to find a second-order stationary point (with small gradient and almost PSD hessian). In this paper, we show that Stabilized SVRG (a simple variant of SVRG) can find an $\epsilon$-second-order stationary point using only $\tilde{O}(n^{2/3}/\epsilon^2 + n/\epsilon^{1.5})$ stochastic gradients. To our best knowledge, this is the first second-order guarantee for a simple variant of SVRG. The running time almost matches the known guarantees for finding $\epsilon$-first-order stationary points. |
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