Timeline for How can it be trapped in a saddle point?
Current License: CC BY-SA 4.0
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| Jun 7, 2019 at 18:26 | comment | added | whuber♦ | Thank you for the reference. A quick glance at it (the link now works) shows the analysis is limited to "strict saddles" (where there are both positive and negative eigenvalues of the Hessian), which precludes many possibilities. The final statements of the paper include "we note that there are very difficult unconstrained optimization problems where the strict saddle condition fails" and they offer quartic minimization as an example. | |
| Jun 7, 2019 at 18:17 | comment | added | Ali Abbasinasab | @whuber you can easily cook up counterexamples. For example if you have only a line as your space. I just tried to add a point which may not be obvious to many (It was initially not too obvious to me why). About the reference, I have no idea why you cannot reach it. I double checked, the link is valid and get updated as well. You may search "Gradient Descent Converges to Minimizers, Jason D. Lee , Max Simchowitz , Michael I. Jordan †, and Benjamin Recht † ♯Department of Electrical Engineering and Computer Sciences †Department of Statistcs University of California, Berkeley, April 19, 2019" | |
| Jun 6, 2019 at 16:55 | comment | added | whuber♦ | I have been unable to reach your link [1]--could you provide a full citation? In the meantime, it is possible to construct counterexamples to your claim, indicating it must be based on additional unstated assumptions. | |
| Jun 6, 2019 at 16:00 | history | edited | Ali Abbasinasab | CC BY-SA 4.0 |
added 5 characters in body
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| Aug 14, 2018 at 11:01 | comment | added | Jan Kukacka | You could just as easily pick a counter-example function where you will get stuck in a saddle point every time... | |
| Jun 9, 2017 at 1:51 | history | answered | Ali Abbasinasab | CC BY-SA 3.0 |