Optimization of EI always gets stuck in local extrema

fgerzer / apsis

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Optimization of EI always gets stuck in local extrema #31

Closed andi1400 closed 9 years ago

andi1400 commented 10 years ago

At the moment we optimize EI with scypy.optimize.minimize. Tried several optimizer methods, all of them get stuck in local extrema.

Problem seems to be well known:

the bergstra group reports on it http://papers.nips.cc/paper/4443-algorithms-for-hyper-parameter-optimization.pdf (page 3)
http://www.icml2010.org/papers/297.pdf report about this, too
the old spearmint package also seems to use grid search here if I understand their code right

Proposed optimization methods there

grid search (probably not feasible)
evolutionary algorithm

Other ideas

random search, how many points?
continue using SLSQP, L-BFGS-B and implement a random restart for them. How often?

bayerj commented 10 years ago

Climin has a recent evolutionary algorithm. https://github.com/BRML/climin/blob/master/climin/nes.py

I say continue with grid search first, solve the problem later.

fgerzer commented 10 years ago

I agree with that. GridSearch (or random search) should suffice for now. After all, the main problem will be inverting the matrix, not evaluating it.

andi1400 commented 10 years ago

~~reminder: at the moment number of grid points for scipy.brute grid search is hard coded!~~ No its not, sorry. My fault.

andi1400 commented 9 years ago

during the work on #34 we switched to using random search as only possibility right now. Keep this in mind when going on here to reenable optimization choice.

andi1400 commented 9 years ago

@andi1400 Document about new EI optimization. Implement optimize_restarts

andi1400 commented 9 years ago

EI Opzimization Improved. We now have implemented EI gradient for use in BFGS optimization of EI. This optimization can be activated setting "acquisition_hyperparams":{"optimization": "bfgs"}.

It will work as follows:

first random search with 1000 samples is executed
the best result found in random search is used as a starting point in BFGS
if BFGS optimization is successful in can only be better than the starting point (can be theoretically proven) => this result will be reported as maximium. In case BFGS was not successful the random search result will be used.

To be done here: Add multiple restarts to BFGS. Make BFGS to be the standard optimizer. Do a bit of performance evaluation to verify results.

fgerzer commented 9 years ago

Closed with the new optimization. For details, see the commits referencing this issue.