physbo.search.score_multi module

physbo.search.score_multi.EHVI(fmean, fstd, pareto)

Calculate Expected Hyper-Volume Improvement (EHVI).

Reference: (Couckuyt et al., 2014) Fast calculation of multiobjective probability of improvement and expected improvement criteria for Pareto optimization

Parameters:

• fmean (numpy.ndarray) – mean of the predictive distribution, shape (N, n_obj); the first axis must be the N candidates, the rest is reshaped to (N, n_obj)

• fstd (numpy.ndarray) – standard deviation of the predictive distribution, any shape with N * n_obj elements (reshaped to (N, n_obj))

• pareto (Pareto object) – Pareto object. The non-dominated region is divided into cells and the reference points are set by default if not done yet.

• objectives (The result is the expected hypervolume improvement when the)

• deviation (are independent normal variables with mean fmean and standard)

• fstd

• contribute (where predictions beyond reference_max in any objective)

• between (zero (they are not clipped). It holds only while the front lies)

• reference_max. (reference_min and)

Returns:

score – score of the candidates, shape (N,)

Return type:

numpy.ndarray

class physbo.search.score_multi.ExpectedHypervolumeImprovement

Bases: object

Callable hypervolume acquisition function wrapping EHVI().

Notes

Called with predictor_list, training, test and pareto as positional arguments. Returns scores of shape (test.X.shape[0],).

See also

EHVI

Acquisition function using posterior means and standard deviations.

name = 'EHVI'

physbo.search.score_multi.HVPI(fmean, fstd, pareto)

Calculate Hypervolume-based Probability of Improvement (HVPI).

Reference: (Couckuyt et al., 2014) Fast calculation of multiobjective probability of improvement and expected improvement criteria for Pareto optimization

Parameters:

• fmean (numpy.ndarray) – mean of the predictive distribution, shape (N, n_obj); the first axis must be the N candidates, the rest is reshaped to (N, n_obj)

• fstd (numpy.ndarray) – standard deviation of the predictive distribution, any shape with N * n_obj elements (reshaped to (N, n_obj))

• pareto (Pareto object) – Pareto object. The non-dominated region is divided into cells and reference_min is set by default if not done yet.

• reference_min. (The result holds only while the front lies above)

Returns:

score – score of the candidates, shape (N,)

Return type:

numpy.ndarray

class physbo.search.score_multi.HypervolumeProbabilityOfImprovement

Bases: object

Callable hypervolume acquisition function wrapping HVPI().

Notes

Called with predictor_list, training, test and pareto as positional arguments. Returns scores of shape (test.X.shape[0],).

See also

HVPI

Acquisition function using posterior means and standard deviations.

name = 'HVPI'

physbo.search.score_multi.TS(predictor_list, training, test, alpha=1, reduced_candidate_num=None, rng=None)

Thompson Sampling for multi-objective optimization.

Parameters:

• predictor_list (list of Predictor) – List of predictors for each objective.

• training (Variable) – Training data containing all objectives.

• test (Variable) – Test points.

• alpha (float, optional) – Scaling parameter for sampling from posterior distribution. Default is 1.

• reduced_candidate_num (int, optional) – Number of candidates to randomly select for Pareto front calculation. If None or less than number of test points, all points are used. Default is None.

Returns:

score_res – Score array with 1 at the chosen index and 0 elsewhere.

Return type:

numpy.ndarray

class physbo.search.score_multi.ThompsonSampling(alpha=1.0, reduced_candidate_num=None, rng=None)

Bases: object

Callable multi-objective Thompson sampling wrapping TS().

Parameters:

• alpha (float, optional) – Posterior sampling scale. Default is 1.0.

• reduced_candidate_num (int, optional) – Maximum number of candidates used for Pareto front calculation. Default is None, which uses all candidates.

• rng (rng object, optional) – Random number generator for the posterior samples and the choice among the Pareto front; None (default) draws from the global numpy.random state. An instance given to a policy without a generator of its own borrows the policy’s (see physbo._rng.attach_rng()).

See also

TS

Multi-objective Thompson sampling acquisition function.

name = 'TS'

physbo.search.score_multi.resolve(score, *, alpha=1.0, reduced_candidate_num=None, rng=None)

Resolve a multi-objective score name or return a callable unchanged.

Parameters:

• score (str or callable) – “EHVI”, “HVPI”, “TS”, or a callable accepting predictor_list, training, test and pareto as positional arguments.

• alpha (float, optional) – Posterior sampling scale for “TS”. Default is 1.0.

• reduced_candidate_num (int, optional) – Candidate limit for “TS”. Default is None, using all candidates.

• rng (rng object, optional) – Random number generator for “TS”. A callable that holds a generator in an rng attribute and was not given one of its own (the built-in ThompsonSampling) is attached to it (see physbo._rng.attach_rng()). Default is None, the global numpy.random state.

Returns:

Acquisition function. Existing callables are returned unchanged.

Return type:

callable

Raises:

• NotImplementedError – If the score name is unknown.

• TypeError – If score is a class rather than an instance, or is neither a string nor a callable.

physbo.search.score_multi.score(mode, predictor_list, test, training, **kwargs)

Calculate multi-objective acquisition scores for test data.

Parameters:

• mode (str or callable) – “EHVI”, “HVPI”, “TS”, or a callable called as mode(predictor_list, training, test, pareto).

• predictor_list (list of predictor objects) – Predictor for each objective.

• test (physbo.Variable) – Test inputs.

• training (physbo.Variable) – Training dataset containing all objectives.

• pareto (Pareto) – Required for EHVI and HVPI. Passed to callable modes, as None when omitted.

• alpha (float) – Posterior sampling scale for string “TS”. Default is 1.0.

• reduced_candidate_num (int or None) – Required candidate limit for string “TS”; None uses all candidates. Callable modes ignore this parameter and alpha.

• rng (rng object) – Random number generator for string “TS” (default: the global numpy.random state); a callable mode draws from its own.

Returns:

Acquisition scores of shape (test.X.shape[0],).

Return type:

numpy.ndarray