The Living Thing / Notebooks : Optimisation, Sequential surrogate; for expensive experiments

Problem statement

According to Gilles Louppe and Manoj Kumar:

We are interested in solving

\begin{equation*} x^* = \arg \min_x f(x) \end{equation*}

under the constraints that

  • \(f\) is a black box for which no closed form is known (nor its gradients);
  • \(f\) is expensive to evaluate;
  • evaluations of \(y=f(x)\) may be noisy.

This is similar to the typical framing of reinforcement learning problems where there is a similar explore/exploit tradeoff, although I do not know the precise disciplinary boundaries that may transect these areas. They both might be thought of as stochastic optimal control problems.

The most common method seems to the “Bayesian optimisation”, which is based on Gaussian Process regressions. However, this is not a requirement, and many possible wacky regression models can give you the surrogate.

Of renewed interest for its use in hyperparameter/model selection, in e.g. regularising complex models. You could also obviously use it in industrial process control, which is where I originally saw this in the form of sequential ANOVA design.

Ben Recht: Random search is competitive with highly tuned bayesian methods in hyperparameter tuning.



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