bayex.acq.expected_improvement

bayex.acq.expected_improvement#

bayex.acq.expected_improvement(x_pred, xs, ys, mask, gp_params, xi=0.01)#

Expected Improvement (EI) acquisition function.

Favors points with high improvement over the current best observed value, balancing exploitation and exploration.

The formula is:

\[EI(x) = (\mu(x) - y^* - \xi) \Phi(z) + \sigma(x) \phi(z)\]

where:

\[z = \frac{\mu(x) - y^* - \xi}{\sigma(x)}\]
Parameters:

  • x_pred (Array) – Candidate input locations to evaluate.

  • xs (Array) – Observed inputs.

  • ys (Array) – Observed function values.

  • mask (Array) – Boolean mask indicating valid entries in ys.

  • gp_params (GPParams) – Gaussian Process hyperparameters.

  • xi (float) – Exploration-exploitation tradeoff parameter.

Returns:

EI scores at x_pred.

Contents