saealib.ParEGOAcquisition

class saealib.ParEGOAcquisition(alpha=0.05, rng=None, direction=None)

ベースクラス: PointwiseAcquisition

ParEGO acquisition function for multi-objective Bayesian optimisation.

Scalarises objectives using the Augmented Tchebycheff function with a randomly sampled weight vector, then applies Expected Improvement on the scalarised prediction (Knowles 2006; a scalarization variant informed by Chugh 2020).

Scalarised objective (minimised):

g(f; w, z*) = max_i [w_i |f_i - z_i*|] + alpha * sum_i w_i |f_i - z_i*|

where z* is the component-wise minimum of the current archive and w is drawn uniformly from the (k-1)-simplex at each call to compute_reference.

Because saealib's ABC receives (n_samples, n_obj) predictions rather than per-objective GP posteriors, the scalarised GP is approximated:

mu_s  = g(mu; w, z*)
std_s = (w . std).sum(axis=-1)   [linear-combination approximation]

EI is then computed on (mu_s, std_s) against the best scalarised archive value.

パラメータ:

• alpha (float) -- Augmentation coefficient (rho in some references). Default: 0.05 (mlr3mbo convention).

• rng (np.random.Generator or None) -- Random number generator for weight sampling.

• direction (np.ndarray or None) -- Per-objective optimization direction (+1 = maximize, -1 = minimize). shape: (n_obj,). archive.f and the predicted mean are converted to minimize-space via direction_to_minimize_sign before the (minimize-only) scalarisation above runs. None (default) means already-minimize; when unset, it is auto-injected from problem.direction at run start.

参照

[29]: Knowles, J. (2006). ParEGO: A hybrid algorithm with on-line landscape approximation for expensive multiobjective optimization problems. IEEE Transactions on Evolutionary Computation, 10(1), 50-66. (Conceptual origin.)

[30]: Chugh, T. (2020). Scalarizing functions in Bayesian multiobjective optimization. 2020 IEEE Congress on Evolutionary Computation (CEC), 1-8. (Scalarization-family reference; saealib uses the weighted augmentation variant documented above.)

Methods

__init__
compute_reference	Sample a new weight vector and compute the ideal point.
contract	Return the ParEGO 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 EI on the Augmented Tchebycheff scalarised prediction.

Method Details

ParEGOAcquisition.__init__(alpha=0.05, rng=None, direction=None)

パラメータ:

• alpha (float)

• rng (Generator | None)

• direction (ndarray | None)

戻り値の型:

None

ParEGOAcquisition.compute_reference(archive, rng=None)

Sample a new weight vector and compute the ideal point.

パラメータ:

• archive (Archive) -- Archive of evaluated solutions.

• rng (np.random.Generator or None, optional) -- Random number generator. When provided (e.g. ctx.rng), it is used instead of the instance-level _rng so all randomness flows through the master RNG.

戻り値:

(z_star, weights, f_best_scalar) — component-wise minimum of archive objective values, a new weight vector drawn uniformly from the (k-1)-simplex, and the minimum scalarised archive value under these weights.

戻り値の型:

tuple

ParEGOAcquisition.contract()

Return the ParEGO acquisition contract.

戻り値の型:

ComponentContract

ParEGOAcquisition.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.

パラメータ:

• candidates_x (np.ndarray)

• prediction (SurrogatePrediction | None)

• archive (Archive)

• ctx (OptimizationState | None)

• prepared (Any)

戻り値の型:

AcquisitionResult

ParEGOAcquisition.prepare(archive, ctx=None)

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

パラメータ:

• archive (Archive)

• ctx (OptimizationState | None)

戻り値の型:

Any

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

Compute EI on the Augmented Tchebycheff scalarised prediction.

パラメータ:

• prediction (SurrogatePrediction) -- Surrogate predictions. Must have std (has_uncertainty == True).

• reference (tuple) -- (z_star, weights, f_best_scalar) from compute_reference.

• rng (Generator | None)

戻り値:

EI scores. shape: (n_samples,). Higher is better.

戻り値の型:

np.ndarray

例外:

TypeError -- If prediction does not contain uncertainty estimates.