saealib.ProductOfFeasibility

class saealib.ProductOfFeasibility

Bases: PointwiseAcquisition

Joint probability of feasibility across all constraint columns.

Computes the product of per-constraint feasibility probabilities:

\[\text{PoF}_{\text{joint}}(x) = \prod_{i=1}^{m} \Phi\!\left(\frac{0 - \mu_i(x)}{\sigma_i(x)}\right)\]

where \(\mu_i\) and \(\sigma_i\) are the surrogate’s predicted mean and standard deviation for the i-th constraint column.

This is the standard acquisition function for constrained Bayesian optimisation with independent constraint surrogates ([23]; Eriksson & Poloczek, 2021). Use it with a surrogate trained on ConstraintObjectiveSet (which returns archive.g as train_y), typically via PerObjectiveSurrogate([GP(), ...] * n_constraints).

Combine this acquisition with an objective acquisition through CompositeAcquisition and configure the result on the optimizer.

Requires a surrogate that provides uncertainty estimates (std).

Notes

Assumes constraints are independent. When constraints are strongly correlated, a multi-output GP with joint predictions is more accurate but is not required by this acquisition function.

References

[23]: Letham, B., Karrer, B., Ottoni, G., & Bakshy, E. (2019). Constrained Bayesian optimization with noisy experiments. Bayesian Analysis, 14(2), 495-519.

Conceptual origin also draws on Eriksson & Poloczek (2021), SCBO.

Methods

__init__
compute_reference	Return None (no reference needed).
contract	Return the pointwise acquisition contract.
evaluate	Reject prediction is None, resolve the reference, then score().
prepare	Delegate to compute_reference(archive, rng=ctx.rng if ctx else None).
score	Compute joint probability of feasibility scores.

Method Details

ProductOfFeasibility.__init__()

ProductOfFeasibility.compute_reference(archive, rng=None)

Return None (no reference needed).

Parameters:

• archive (Archive)

• rng (np.random.Generator | None)

Return type:

Any

ProductOfFeasibility.contract()

Return the pointwise acquisition contract.

Return type:

ComponentContract

ProductOfFeasibility.evaluate(candidates_x, prediction, archive, ctx=None, *, prepared=<object object>)

Reject prediction is None, resolve the reference, then score().

See AcquisitionFunction.evaluate() for the shared parameter contract, including the _UNSET vs. explicit prepared=None distinction.

Parameters:

• candidates_x (np.ndarray)

• prediction (SurrogatePrediction | None)

• archive (Archive)

• ctx (OptimizationState | None)

• prepared (Any)

Return type:

AcquisitionResult

ProductOfFeasibility.prepare(archive, ctx=None)

Delegate to compute_reference(archive, rng=ctx.rng if ctx else None).

Parameters:

• archive (Archive)

• ctx (OptimizationState | None)

Return type:

Any

ProductOfFeasibility.score(prediction, reference=None, rng=None)

Compute joint probability of feasibility scores.

Parameters:

• prediction (SurrogatePrediction) – Surrogate predictions of constraint values. prediction.value shape: (n_samples, n_constraints). Must have std (has_uncertainty == True).

• reference (Any) – Not used. Accepted for interface compatibility.

• rng (Generator | None)

Returns:

Joint PoF scores in [0, 1]. shape: (n_samples,). Score is 1 when all constraints are clearly satisfied, 0 when any constraint is clearly violated.

Return type:

np.ndarray

Raises:

TypeError – If prediction does not contain uncertainty estimates.