Acquisition Functions

Acquisition functions guide the selection of next experiments in Bayesian optimization. They balance exploration (reducing uncertainty) and exploitation (targeting optimal regions).

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BoTorch Acquisition

PyTorch-based acquisition functions with batch support.

alchemist_core.acquisition.botorch_acquisition.BoTorchAcquisition(search_space, model=None, acq_func='ucb', maximize=True, random_state=42, acq_func_kwargs=None, batch_size=1, ref_point=None, directions=None, objective_names=None, outcome_constraints=None)

Bases: BaseAcquisition

Acquisition function implementation using BoTorch.

Supported acquisition functions: - 'ei': Expected Improvement - 'logei': Log Expected Improvement (numerically stable) - 'pi': Probability of Improvement - 'logpi': Log Probability of Improvement (numerically stable) - 'ucb': Upper Confidence Bound - 'qei': Batch Expected Improvement (for q>1) - 'qucb': Batch Upper Confidence Bound (for q>1) - 'qipv' or 'qnipv': q-Negative Integrated Posterior Variance (exploratory)

Initialize the BoTorch acquisition function.

Parameters:

Name	Type	Description	Default
search_space		The search space (SearchSpace object)	required
model		A trained model (BoTorchModel)	None
acq_func		Acquisition function type (see class docstring for options)	'ucb'
maximize		Whether to maximize (True) or minimize (False) the objective	True
random_state		Random state for reproducibility	42
acq_func_kwargs		Dictionary of additional arguments for the acquisition function	None
batch_size		Number of points to select at once (q)	1
ref_point		Reference point for MOBO hypervolume (list of floats)	None
directions		Per-objective direction list ('maximize'/'minimize')	None
objective_names		List of objective names (for multi-objective)	None
outcome_constraints		List of outcome constraint callables for MOBO	None

Raises:

Type	Description
ValueError	If acq_func is not a valid acquisition function name

select_next(candidate_points=None)

Suggest the next experiment point(s) using BoTorch optimization.

Parameters:

Name	Type	Description	Default
candidate_points		Candidate points to evaluate (optional)	None

Returns:

Type	Description
	Dictionary with the selected point or list of points

find_optimum(model=None, maximize=None, random_state=None)

Find the point where the model predicts the optimal value.

This uses the same approach as regret plot predictions: generate a grid in the original variable space, predict using the model's standard pipeline, and find the argmax/argmin. This ensures categorical variables are handled correctly through proper encoding/decoding.

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Skopt Acquisition

Scikit-optimize based acquisition functions.

alchemist_core.acquisition.skopt_acquisition.SkoptAcquisition(search_space, model=None, acq_func='ei', maximize=True, random_state=42, acq_func_kwargs=None)

Bases: BaseAcquisition

Simple acquisition function implementation using scikit-optimize (skopt).

Supported acquisition functions: - 'ei' or 'EI': Expected Improvement - 'pi' or 'PI': Probability of Improvement
- 'ucb' or 'UCB': Upper Confidence Bound (mapped to LCB in skopt) - 'gp_hedge': GP-Hedge (portfolio of acquisition functions)

Initialize the acquisition function.

Parameters:

Name	Type	Description	Default
search_space		The search space (SearchSpace object or list of skopt dimensions)	required
model		A trained model (SklearnModel or compatible)	None
acq_func		Acquisition function ('ei', 'pi', 'ucb', or 'gp_hedge')	'ei'
maximize		Whether to maximize (True) or minimize (False) the objective	True
random_state		Random state for reproducibility	42
acq_func_kwargs		Dictionary of additional arguments for the acquisition function	None

Raises:

Type	Description
ValueError	If acq_func is not a valid acquisition function name

select_next(candidate_points=None, **kwargs)

Suggest the next experiment point.

find_optimum(model, maximize=True, random_state=42)

Find the point where the model predicts the optimal value.

Parameters:

Name	Type	Description	Default
model		Trained model with predict method	required
maximize		Whether to maximize (True) or minimize (False) the objective	True
random_state		Random seed for reproducibility	42

Returns:

Name	Type	Description
dict		Contains 'x_opt' (optimal point), 'value' (predicted value), 'std' (standard deviation at optimum)

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Available Strategies

Single-Point Strategies

Strategy	Code	Description	Best For
Expected Improvement	'EI'	Balances exploration/exploitation	General use
Log EI	'LogEI'	Numerically stable EI	Noisy data
Probability of Improvement	'PI'	Conservative improvement	Risk-averse
Log PI	'LogPI'	Numerically stable PI	Noisy data
Upper Confidence Bound	'UCB'	More exploratory	Unknown spaces

Batch Strategies

Strategy	Code	Description	Best For
Batch Expected Improvement	'qEI'	Parallel experiments	Lab workflows
Batch UCB	'qUCB'	Parallel + exploratory	Exploration
Negative Integrated Posterior Variance	'qNIPV'	Pure exploration	Model improvement

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See Also

• OptimizationSession - High-level acquisition interface
• BoTorch Acquisition Guide - Detailed strategy explanations
• Models - Model training for acquisition