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I have a very expensive black-box function and at least 15 parameters that I want to explore (usually 5-6 at a time). So far I have tried Genetic Algorithms and Gaussian Process Surrogate Optimization (bayesian optimization). Both methods work fine and efficiently up to 5-6 parameters. However, I am having an issue on how can one be sure that a solution found by GA/GPSO is a good solution, without basically knowing nothing about the output space. I don't really want to go for an exhaustive grid search since even with 5 parameters, it requires incredible amounts of evaluations, yet I cannot come up with anything better.

I would also very much appreciate suggestions/keywords for literature reading, or event different methods for hyperparameter optimizations.

Thanks in advance

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The short answer: You can't. These are heuristics. There are no guarantees. They might fail badly; and there's no reliable way to detect that.

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  • $\begingroup$ I think in one article, they were showing for GPSO that it converges %70 of times (with toy data set I believe), and making an argument on that. Are you aware of such a method? PS: I'll send a link to paper / explain it better $\endgroup$ – b.y Apr 2 '20 at 17:01
  • $\begingroup$ @b.y, those are presumably empirical results. Also that presumably means that 30% of the time it didn't work well. Not very helpful if I have a single problem I want to solve; it will give me a proposed solution, but did that fall into the category where it worked well or where it didn't? No reliable way to know for sure. $\endgroup$ – D.W.♦ Apr 2 '20 at 17:58

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