Closely related is AutoML
According to Gilles Louppe and Manoj Kumar:
We are interested in solving
$$ x^* = \arg \min_x f(x) $$
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 optimisation surrogate.
Of renewed interest for its use in hyperparameter/model selection, in e.g. regularising complex models, which is compactly referred to these days as automl.
You could also obviously use it in industrial process control, which is where I originally saw this kind of thing, in the form of sequential ANOVA design, which is an incredible idea itself, although that is now years old so is not nearly so hip. Since this effectively an attempt at optimal, nonlinear, heteroskedastic sequential ANOVA, I am led to wonder if we can dispense with ANOVA now. Does this stuff actually work well enough? Or is it the same thing, repackaged?
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- LJDR16: Lisha Li, Kevin Jamieson, Giulia DeSalvo, Afshin Rostamizadeh, Ameet Talwalkar (2016) Hyperband: A Novel Bandit-Based Approach to Hyperparameter Optimization. ArXiv:1603.06560 [Cs, Stat].
- SSZA14: Jasper Snoek, Kevin Swersky, Rich Zemel, Ryan Adams (2014) Input Warping for Bayesian Optimization of Non-Stationary Functions. In Proceedings of the 31st International Conference on Machine Learning (ICML-14) (pp. 1674–1682).
- SwSA13: Kevin Swersky, Jasper Snoek, Ryan P Adams (2013) Multi-Task Bayesian Optimization. In Advances in Neural Information Processing Systems 26 (pp. 2004–2012). Curran Associates, Inc.
- ALSW17: Zeyuan Allen-Zhu, Yuanzhi Li, Aarti Singh, Yining Wang (2017) Near-Optimal Design of Experiments via Regret Minimization. In PMLR (pp. 126–135).
- Močk75: J. Močkus (1975) On Bayesian Methods for Seeking the Extremum. In Optimization Techniques IFIP Technical Conference (pp. 400–404). Springer Berlin Heidelberg DOI
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