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- W4321177620 abstract "We prove that various stochastic gradient descent methods, including the stochastic gradient descent (SGD), stochastic heavy-ball (SHB), and stochastic Nesterov's accelerated gradient (SNAG) methods, almost surely avoid any strict saddle manifold. To the best of our knowledge, this is the first time such results are obtained for SHB and SNAG methods. Moreover, our analysis expands upon previous studies on SGD by removing the need for bounded gradients of the objective function and uniformly bounded noise. Instead, we introduce a more practical local boundedness assumption for the noisy gradient, which is naturally satisfied in empirical risk minimization problems typically seen in training of neural networks." @default.
- W4321177620 created "2023-02-18" @default.
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- W4321177620 date "2023-02-15" @default.
- W4321177620 modified "2023-09-25" @default.
- W4321177620 title "Almost Sure Saddle Avoidance of Stochastic Gradient Methods without the Bounded Gradient Assumption" @default.
- W4321177620 doi "https://doi.org/10.48550/arxiv.2302.07862" @default.
- W4321177620 hasPublicationYear "2023" @default.
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