Post #3030809

2025-05-15 08:35 UTC

@tao@mathstodon.xyz sounds like it would help to quantify the roughness of the function. Smooth analytic functions are easier to extremise than fractals, which are easier than even rougher functions. Comes down to the asymptotic behaviour of its power spectrum. They typically require different optimisers. On the other hand, this roughness may very in space and with scale, making the problem harder. It may even vary non-smoothly with these!

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@tao@mathstodon.xyz 2025-05-15 15:17

@TomL@mathstodon.xyz One of the advantages of this particular tool is that it is agnostic with respect to these sorts of decisions that would otherwise be handled by manually selected hyperparameters. For instance, it may initially try optimization methods that work well for smooth functions, but at some point discover that rougher functions are outperforming, at which point it can automatically switch its selected methods to those that work better for rough functions. (Though sometimes it can get stuck in "local maxima" in which the less appropriate, but highly optimized, method is outperforming a more appropriate, but not yet optimized method, and some manual intervention at that point is required.)

Open ##3030810