# Background¶

## Theory¶

Osprey is designed to optimize the hyperparameters of machine learning models by maximizing a cross-validation score. As an optimization problem, the key factors here are

• very expensive objective function evaluations (minutes to hours, or more)
• no gradient information is available
• tension between exploration of parameter space and local optimization (explore / exploit dilemma)

A good, if somewhat dated overview of this problem setting can be found in Jones, Schonlau, Welch (1998) [1]. The key idea is that we can procede by fitting a surrogate function or response surface. This surrogate function needs to provide both our best guess of the function as well as our degree of belief – our uncertainty in the parts of parameter space that we haven’t yet explored. Does the maxima lie over there? Then at each iteration, a new point can be selected by maximizing the expected improvement over our current best solution, by maximize the expected entropy reduction in the distribution of maxima, [3] or a similar so-called acquisition function.

osprey supports multiple search strategies for choosing the next set of hyperparameters to evaluate your model at. The most theoretically elegant of the supported methods, Gaussian process expected improvement using the MOE backend, attacks this problem directly by modeling the objective function as a draw from a Gaussian process.

## References¶

 [1] Jones, D. R., M. Schonlau, and W. J. Welch. “Efficient global optimization of expensive black-box functions.” J. Global Optim. 13.4 (1998): 455-492.
 [2] Bergstra, James S., et al. “Algorithms for hyper-parameter optimization.” NIPS. 2011.
 [3] Hennig, P., and C. J. Schuler. “Entropy search for information-efficient global optimization.” JMLR 98888.1 (2012): 1809-1837.
 [4] Snoek, J., H. Larochelle, and R. P. Adams. “Practical Bayesian optimization of machine learning algorithms.” NIPS 2012.