In conversation at #CHR2024 the question that came up often was: If we solve a problem by prompting, how do we know when we have optimized the solution? You can’t do a grid search to find optimal hyperparameters if your search space is All of Language.
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The correct answer is not to do a grid search at all, but treat this like an optimization problem.
I guess this could be a viable solution as long as we feel some confidence that our prompts are spread out well in the space of possibility, not all clustered in one corner.
For many hyperparam spaces deciding which axes are log and which are linear is nonobvious
Random Search for Hyper-Parameter Optimization 2012 https://www.jmlr.org/papers/volume13/bergstra12a/bergstra12a.pdf