First-order methods almost always avoid strict saddle points

Mathematical Programming, pp. 1-27, 2019.

Cited by: 166|Views106
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Abstract:

We establish that first-order methods avoid strict saddle points for almost all initializations. Our results apply to a wide variety of first-order methods, including (manifold) gradient descent, block coordinate descent, mirror descent and variants thereof. The connecting thread is that such algorithms can be studied from a dynamical sys...More

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