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Probability Of Improvement

ProbabilityOfImprovement dataclass 

ProbabilityOfImprovement()

Bases: AbstractSinglePointUtilityFunctionBuilder

An acquisition function which returns the probability of improvement of the objective function over the best observed value.

More precisely, given a predictive posterior distribution of the objective function ff, the probability of improvement at a test point xx is defined as: \(PI(x)=Prob[f(x)<f(xbest)]\text{PI}(x) = \text{Prob}[f(x) < f(x_{\text{best}})]\) where xbestx_{\text{best}} is the minimiser of the posterior mean at previously observed values (to handle noisy observations).

The probability of improvement can be easily computed using the cumulative distribution function of the standard normal distribution Ξ¦\Phi: \(PI(x)=Ξ¦(f(xbest)βˆ’ΞΌΟƒ)\text{PI}(x) = \Phi\left(\frac{f(x_{\text{best}}) - \mu}{\sigma}\right)\) where ΞΌ\mu and Οƒ\sigma are the mean and standard deviation of the predictive distribution of the objective function at xx.

References

[1] Kushner, H. J. (1964). A new method of locating the maximum point of an arbitrary multipeak curve in the presence of noise. Journal of Basic Engineering, 86(1), 97-106.

[2] Shahriari, B., Swersky, K., Wang, Z., Adams, R. P., & de Freitas, N. (2016). Taking the human out of the loop: A review of Bayesian optimization. Proceedings of the IEEE, 104(1), 148-175. doi: 10.1109/JPROC.2015.2494218

check_objective_present 

check_objective_present(posteriors, datasets)

Check that the objective posterior and dataset are present in the posteriors and datasets.

Parameters:

  • posteriors (Mapping[str, AbstractPosterior]) –

    dictionary of posteriors to be used to form the utility function.

  • datasets (Mapping[str, Dataset]) –

    dictionary of datasets which may be used to form the utility function.

Raises:

  • ValueError –

    If the objective posterior or dataset are not present in the posteriors or datasets.

build_utility_function 

build_utility_function(posteriors, datasets, key)

Constructs the probability of improvement utility function using the predictive posterior of the objective function.

Parameters:

  • posteriors (Mapping[str, AbstractPosterior]) –

    Dictionary of posteriors to be

  • datasets (Mapping[str, Dataset]) –

    Dictionary of datasets which may be used

  • key (KeyArray) –

    JAX PRNG key used for random number generation. Since

Returns: