Convergence/Divergence

[bayerj]

So we had that issue yesterday that climin should never stop iterating because it thinks it converged. However, it might happen that it diverges and that that needs to be handled.

E.g. I am currently playing around with logistic regression and NCG which sometimes diverges because the direction becomes invalid (e.g. NaN).

What is the best behaviour here?

• throw a Diverged exception?
• stop iterating?
• try to recover via heuristics?
• just continue and let the user find out via inspection of info?

[rueckstiess]

there could be a "diverged" stop criterion as well. the problem would then be a special case of the whole stopping mechanism and shouldn't be handled by the minimizer explicitly. so that would be suggestion 4 "just continue".

but i don't know if an external stop criterion can always decide that the algorithm diverged only based on the info dict. perhaps the minimizer knows that best. in that case i'd probably vote for 1 "throw exception".

[bayerj]

The difference here is, that divergence can actually be harmfull.

If we converge, running longer does not do any harm since our solution
will not get worse. If we diverge, the following operations might
overwrite the current wrt with a mess, result in infinite line
searches or throw a numpy error.

Thus, a divergence stopping criterion would be the default... but that
could be ok.

2012/2/28 Thomas Rückstieß
[email protected]:

there could be a "diverged" stop criterion as well. the problem would then be a special case of the whole stopping mechanism and shouldn't be handled by the minimizer explicitly. so that would be suggestion 4 "just continue".

but i don't know if an external stop criterion can always decide that the algorithm diverged only based on the info dict. perhaps the minimizer knows that best. in that case i'd probably vote for 1 "throw exception".

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Dipl. Inf. Justin Bayer
Lehrstuhl für Robotik und Echtzeitsysteme, Technische Universität München
http://www6.in.tum.de/Main/Bayerj