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We consider the case of derivative-free algorithms for non-convex optimization, also known as zero order algorithms, that use only function evaluations rather than gradients.
Some np-complete problems in quadratic and nonlinear programming
Katta G. Murty and Santosh N. Kabadi · 1987
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Global stability of dynamical systems
Michael Shub · 1987
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Stochastic first- and zeroth-order methods for nonconvex stochastic programming
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Identifying and attacking the saddle point problem in high-dimensional non-convex optimization
Yann N. Dauphin, Razvan Pascanu, Çaglar Gülçehre, KyungHyun Cho, Surya Ganguli, and Yoshua Bengio · 2014
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The loss surfaces of multilayer networks
Anna Choromanska, Mikael Henaff, Michaël Mathieu, Gérard Ben Arous, and Yann LeCun · 2015
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Optimal rates for zero-order convex optimization: The power of two function evaluations
John C. Duchi, Michael I. Jordan, Martin J. Wainwright, and Andre Wibisono · 2015
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Structured evolution with compact architectures for scalable policy optimization
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Gradient descent can take exponential time to escape saddle points
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Stochastic zeroth-order optimization in high dimensions
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First-order methods almost always avoid strict saddle points
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