ax.models¶
Base Models¶
ax.models.discrete_base module¶

class
ax.models.discrete_base.
DiscreteModel
[source]¶ Bases:
ax.models.base.Model
This class specifies the interface for a model based on discrete parameters.
These methods should be implemented to have access to all of the features of Ax.

best_point
(n, parameter_values, objective_weights, outcome_constraints=None, fixed_features=None, pending_observations=None, model_gen_options=None)[source]¶ Obtains the point that has the best value according to the model prediction and its model predictions.

cross_validate
(Xs_train, Ys_train, Yvars_train, X_test)[source]¶ Do cross validation with the given training and test sets.
Training set is given in the same format as to fit. Test set is given in the same format as to predict.
 Parameters
Xs_train (
List
[List
[List
[Union
[str
,float
,int
,None
]]]]) – A list of m lists X of parameterizations (each parameterization is a list of parameter values of length d), each of length k_i, for each outcome.Ys_train (
List
[List
[float
]]) – The corresponding list of m lists Y, each of length k_i, for each outcome.Yvars_train (
List
[List
[float
]]) – The variances of each entry in Ys, same shape.X_test (
List
[List
[Union
[str
,float
,int
,None
]]]) – List of the j parameterizations at which to make predictions.
 Return type
Tuple
[ndarray
,ndarray
] Returns
2element tuple containing
(j x m) array of outcome predictions at X.
(j x m x m) array of predictive covariances at X. cov[j, m1, m2] is Cov[m1@j, m2@j].

fit
(Xs, Ys, Yvars, parameter_values, outcome_names)[source]¶ Fit model to m outcomes.
 Parameters
Xs (
List
[List
[List
[Union
[str
,float
,int
,None
]]]]) – A list of m lists X of parameterizations (each parameterization is a list of parameter values of length d), each of length k_i, for each outcome.Ys (
List
[List
[float
]]) – The corresponding list of m lists Y, each of length k_i, for each outcome.Yvars (
List
[List
[float
]]) – The variances of each entry in Ys, same shape.parameter_values (
List
[List
[Union
[str
,float
,int
,None
]]]) – A list of possible values for each parameter.
 Return type
None

gen
(n, parameter_values, objective_weights, outcome_constraints=None, fixed_features=None, pending_observations=None, model_gen_options=None)[source]¶ Generate new candidates.
 Parameters
n (
int
) – Number of candidates to generate.parameter_values (
List
[List
[Union
[str
,float
,int
,None
]]]) – A list of possible values for each parameter.objective_weights (
Optional
[ndarray
]) – The objective is to maximize a weighted sum of the columns of f(x). These are the weights.outcome_constraints (
Optional
[Tuple
[ndarray
,ndarray
]]) – A tuple of (A, b). For k outcome constraints and m outputs at f(x), A is (k x m) and b is (k x 1) such that A f(x) <= b.fixed_features (
Optional
[Dict
[int
,Union
[str
,float
,int
,None
]]]) – A map {feature_index: value} for features that should be fixed to a particular value during generation.pending_observations (
Optional
[List
[List
[List
[Union
[str
,float
,int
,None
]]]]]) – A list of m lists of parameterizations (each parameterization is a list of parameter values of length d), each of length k_i, for each outcome i.model_gen_options (
Optional
[Dict
[str
,Union
[int
,float
,str
,AcquisitionFunction
]]]) – A config dictionary that can contain modelspecific options.
 Return type
Tuple
[List
[List
[Union
[str
,float
,int
,None
]]],List
[float
]] Returns
2element tuple containing
List of n generated points, where each point is represented by a list of parameter values.
List of weights for each of the n points.

predict
(X)[source]¶ Predict
 Parameters
X (
List
[List
[Union
[str
,float
,int
,None
]]]) – List of the j parameterizations at which to make predictions. Return type
Tuple
[ndarray
,ndarray
] Returns
2element tuple containing
(j x m) array of outcome predictions at X.
(j x m x m) array of predictive covariances at X. cov[j, m1, m2] is Cov[m1@j, m2@j].

update
(Xs, Ys, Yvars, parameter_values, outcome_names)[source]¶ Update model with new data. Note that this data will be treated as new even if the model has already been fit to it, so ensure that only new data is passed in or use fit to refit the model from scratch.
 Parameters
Xs (
List
[List
[List
[Union
[str
,float
,int
,None
]]]]) – A list of m lists X of parameterizations (each parameterization is a list of parameter values of length d), each of length k_i, for each outcome.Ys (
List
[List
[float
]]) – The corresponding list of m lists Y, each of length k_i, for each outcome.Yvars (
List
[List
[float
]]) – The variances of each entry in Ys, same shape.parameter_values (
List
[List
[Union
[str
,float
,int
,None
]]]) – A list of possible values for each parameter.
 Return type
None

ax.models.model_utils module¶

ax.models.model_utils.
add_fixed_features
(tunable_points, d, fixed_features, tunable_feature_indices)[source]¶ Add fixed features to points in tunable space.
 Parameters
tunable_points (
ndarray
) – Points in tunable space.d (
int
) – Dimension of parameter space.fixed_features (
Optional
[Dict
[int
,float
]]) – A map {feature_index: value} for features that should be fixed to a particular value during generation.tunable_feature_indices (
ndarray
) – Parameter indices (in d) which are tunable.
 Returns
Points in the full ddimensional space, defined by bounds.
 Return type
points

ax.models.model_utils.
as_array
(x)[source]¶ Convert every item in a tuple of tensors/arrays into an array.

ax.models.model_utils.
best_observed_point
(model, bounds, objective_weights, outcome_constraints=None, linear_constraints=None, fixed_features=None, options=None)[source]¶ Select the best point that has been observed.
Implements two approaches to selecting the best point.
For both approaches, only points that satisfy parameter space constraints (bounds, linear_constraints, fixed_features) will be returned. Points must also be observed for all objective and constraint outcomes. Returned points may violate outcome constraints, depending on the method below.
1: Select the point that maximizes the expected utility (objective_weights^T posterior_objective_means  baseline) * Prob(feasible) Here baseline should be selected so that at least one point has positive utility. It can be specified in the options dict, otherwise min (objective_weights^T posterior_objective_means) will be used, where the min is over observed points.
2: Select the bestobjective point that is feasible with at least probability p.
The following quantities may be specified in the options dict:
best_point_method: ‘max_utility’ (default) or ‘feasible_threshold’ to select between the two approaches described above.
utility_baseline: Value for the baseline used in max_utility approach. If not provided, defaults to min objective value.
probability_threshold: Threshold for the feasible_threshold approach. Defaults to p=0.95.
feasibility_mc_samples: Number of MC samples used for estimating the probability of feasibility (defaults 10k).
 Parameters
model (
Union
[NumpyModel
,TorchModel
]) – Numpy or Torch model.bounds (
List
[Tuple
[float
,float
]]) – A list of (lower, upper) tuples for each feature.objective_weights (
Union
[Tensor
,ndarray
,None
]) – The objective is to maximize a weighted sum of the columns of f(x). These are the weights.outcome_constraints (
Optional
[Tuple
[Union
[Tensor
,ndarray
],Union
[Tensor
,ndarray
]]]) – A tuple of (A, b). For k outcome constraints and m outputs at f(x), A is (k x m) and b is (k x 1) such that A f(x) <= b.linear_constraints (
Optional
[Tuple
[Union
[Tensor
,ndarray
],Union
[Tensor
,ndarray
]]]) – A tuple of (A, b). For k linear constraints on ddimensional x, A is (k x d) and b is (k x 1) such that A x <= b.fixed_features (
Optional
[Dict
[int
,float
]]) – A map {feature_index: value} for features that should be fixed to a particular value in the best point.options (
Optional
[Dict
[str
,Union
[int
,float
,str
,AcquisitionFunction
]]]) – A config dictionary with settings described above.
 Return type
Optional
[ndarray
] Returns
A darray of the best point, or None if no feasible point exists.

ax.models.model_utils.
check_duplicate
(point, points)[source]¶ Check if a point exists in another array.
 Parameters
point (
ndarray
) – Newly generated point to check.prev_points – Points previously generated.
 Return type
 Returns
True if the point is contained in points, else False

ax.models.model_utils.
check_param_constraints
(linear_constraints, point)[source]¶ Check if a point satisfies parameter constraints.
 Parameters
linear_constraints (
Tuple
[ndarray
,ndarray
]) – A tuple of (A, b). For k linear constraints on ddimensional x, A is (k x d) and b is (k x 1) such that A x <= b.point (
ndarray
) – A candidate point in ddimensional space, as a (1 x d) matrix.
 Return type
 Returns
2element tuple containing
Flag that is True if all constraints are satisfied by the point.
Indices of constraints which are violated by the point.

ax.models.model_utils.
filter_constraints_and_fixed_features
(X, bounds, linear_constraints=None, fixed_features=None)[source]¶ Filter points to those that satisfy bounds, linear_constraints, and fixed_features.
 Parameters
X (
Union
[Tensor
,ndarray
]) – An tensor or array of points.bounds (
List
[Tuple
[float
,float
]]) – A list of (lower, upper) tuples for each feature.linear_constraints (
Optional
[Tuple
[Union
[Tensor
,ndarray
],Union
[Tensor
,ndarray
]]]) – A tuple of (A, b). For k linear constraints on ddimensional x, A is (k x d) and b is (k x 1) such that A x <= b.fixed_features (
Optional
[Dict
[int
,float
]]) – A map {feature_index: value} for features that should be fixed to a particular value in the best point.
 Return type
Union
[Tensor
,ndarray
] Returns
Feasible points.

ax.models.model_utils.
get_observed
(Xs, objective_weights, outcome_constraints=None)[source]¶ Filter points to those that are observed for objective outcomes and outcomes that show up in outcome_constraints (if there are any).
 Parameters
Xs (
Union
[List
[Tensor
],List
[ndarray
]]) – A list of m (k_i x d) feature matrices X. Number of rows k_i can vary from i=1,…,m.objective_weights (
Union
[Tensor
,ndarray
]) – The objective is to maximize a weighted sum of the columns of f(x). These are the weights.outcome_constraints (
Optional
[Tuple
[Union
[Tensor
,ndarray
],Union
[Tensor
,ndarray
]]]) – A tuple of (A, b). For k outcome constraints and m outputs at f(x), A is (k x m) and b is (k x 1) such that A f(x) <= b.
 Return type
Union
[Tensor
,ndarray
] Returns
Points observed for all objective outcomes and outcome constraints.

ax.models.model_utils.
rejection_sample
(gen_unconstrained, n, d, tunable_feature_indices, linear_constraints=None, deduplicate=False, max_draws=None, fixed_features=None, rounding_func=None, existing_points=None)[source]¶ Rejection sample in parameter space.
Models must implement a gen_unconstrained method in order to support rejection sampling via this utility.

ax.models.model_utils.
tunable_feature_indices
(bounds, fixed_features=None)[source]¶ Get the feature indices of tunable features.
 Parameters
 Return type
ndarray
 Returns
The indices of tunable features.
ax.models.numpy_base module¶

class
ax.models.numpy_base.
NumpyModel
[source]¶ Bases:
ax.models.base.Model
This class specifies the interface for a numpybased model.
These methods should be implemented to have access to all of the features of Ax.

best_point
(bounds, objective_weights, outcome_constraints=None, linear_constraints=None, fixed_features=None, model_gen_options=None)[source]¶ Identify the current best point, satisfying the constraints in the same format as to gen.
Return None if no such point can be identified.
 Parameters
bounds (
List
[Tuple
[float
,float
]]) – A list of (lower, upper) tuples for each column of X.objective_weights (
ndarray
) – The objective is to maximize a weighted sum of the columns of f(x). These are the weights.outcome_constraints (
Optional
[Tuple
[ndarray
,ndarray
]]) – A tuple of (A, b). For k outcome constraints and m outputs at f(x), A is (k x m) and b is (k x 1) such that A f(x) <= b.linear_constraints (
Optional
[Tuple
[ndarray
,ndarray
]]) – A tuple of (A, b). For k linear constraints on ddimensional x, A is (k x d) and b is (k x 1) such that A x <= b.fixed_features (
Optional
[Dict
[int
,float
]]) – A map {feature_index: value} for features that should be fixed to a particular value in the best point.model_gen_options (
Optional
[Dict
[str
,Union
[int
,float
,str
,AcquisitionFunction
]]]) – A config dictionary that can contain modelspecific options.
 Return type
Optional
[ndarray
] Returns
A darray of the best point.

cross_validate
(Xs_train, Ys_train, Yvars_train, X_test)[source]¶ Do cross validation with the given training and test sets.
Training set is given in the same format as to fit. Test set is given in the same format as to predict.
 Parameters
Xs_train (
List
[ndarray
]) – A list of m (k_i x d) feature matrices X. Number of rows k_i can vary from i=1,…,m.Ys_train (
List
[ndarray
]) – The corresponding list of m (k_i x 1) outcome arrays Y, for each outcome.Yvars_train (
List
[ndarray
]) – The variances of each entry in Ys, same shape.X_test (
ndarray
) – (j x d) array of the j points at which to make predictions.
 Return type
Tuple
[ndarray
,ndarray
] Returns
2element tuple containing
(j x m) array of outcome predictions at X.
(j x m x m) array of predictive covariances at X. cov[j, m1, m2] is Cov[m1@j, m2@j].

fit
(Xs, Ys, Yvars, bounds, task_features, feature_names, fidelity_features)[source]¶ Fit model to m outcomes.
 Parameters
Xs (
List
[ndarray
]) – A list of m (k_i x d) feature matrices X. Number of rows k_i can vary from i=1,…,m.Ys (
List
[ndarray
]) – The corresponding list of m (k_i x 1) outcome arrays Y, for each outcome.Yvars (
List
[ndarray
]) – The variances of each entry in Ys, same shape.bounds (
List
[Tuple
[float
,float
]]) – A list of d (lower, upper) tuples for each column of X.task_features (
List
[int
]) – Columns of X that take integer values and should be treated as task parameters.fidelity_features (
List
[int
]) – Columns of X that should be treated as fidelity parameters.
 Return type
None

gen
(n, bounds, objective_weights, outcome_constraints=None, linear_constraints=None, fixed_features=None, pending_observations=None, model_gen_options=None, rounding_func=None)[source]¶ Generate new candidates.
 Parameters
n (
int
) – Number of candidates to generate.bounds (
List
[Tuple
[float
,float
]]) – A list of (lower, upper) tuples for each column of X.objective_weights (
ndarray
) – The objective is to maximize a weighted sum of the columns of f(x). These are the weights.outcome_constraints (
Optional
[Tuple
[ndarray
,ndarray
]]) – A tuple of (A, b). For k outcome constraints and m outputs at f(x), A is (k x m) and b is (k x 1) such that A f(x) <= b.linear_constraints (
Optional
[Tuple
[ndarray
,ndarray
]]) – A tuple of (A, b). For k linear constraints on ddimensional x, A is (k x d) and b is (k x 1) such that A x <= b.fixed_features (
Optional
[Dict
[int
,float
]]) – A map {feature_index: value} for features that should be fixed to a particular value during generation.pending_observations (
Optional
[List
[ndarray
]]) – A list of m (k_i x d) feature arrays X for m outcomes and k_i pending observations for outcome i.model_gen_options (
Optional
[Dict
[str
,Union
[int
,float
,str
,AcquisitionFunction
]]]) – A config dictionary that can contain modelspecific options.rounding_func (
Optional
[Callable
[[ndarray
],ndarray
]]) – A function that rounds an optimization result (xbest) appropriately (i.e., according to roundtrip transformations)
 Return type
Tuple
[ndarray
,ndarray
] Returns
2element tuple containing
(n x d) array of generated points.
narray of weights for each point.

predict
(X)[source]¶ Predict
 Parameters
X (
ndarray
) – (j x d) array of the j points at which to make predictions. Return type
Tuple
[ndarray
,ndarray
] Returns
2element tuple containing
(j x m) array of outcome predictions at X.
(j x m x m) array of predictive covariances at X. cov[j, m1, m2] is Cov[m1@j, m2@j].

ax.models.torch_base module¶

class
ax.models.torch_base.
TorchModel
[source]¶ Bases:
ax.models.base.Model
This class specifies the interface for a torchbased model.
These methods should be implemented to have access to all of the features of Ax.

best_point
(bounds, objective_weights, outcome_constraints=None, linear_constraints=None, fixed_features=None, model_gen_options=None)[source]¶ Identify the current best point, satisfying the constraints in the same format as to gen.
Return None if no such point can be identified.
 Parameters
bounds (
List
[Tuple
[float
,float
]]) – A list of (lower, upper) tuples for each column of X.objective_weights (
Tensor
) – The objective is to maximize a weighted sum of the columns of f(x). These are the weights.outcome_constraints (
Optional
[Tuple
[Tensor
,Tensor
]]) – A tuple of (A, b). For k outcome constraints and m outputs at f(x), A is (k x m) and b is (k x 1) such that A f(x) <= b.linear_constraints (
Optional
[Tuple
[Tensor
,Tensor
]]) – A tuple of (A, b). For k linear constraints on ddimensional x, A is (k x d) and b is (k x 1) such that A x <= b.fixed_features (
Optional
[Dict
[int
,float
]]) – A map {feature_index: value} for features that should be fixed to a particular value in the best point.model_gen_options (
Optional
[Dict
[str
,Union
[int
,float
,str
,AcquisitionFunction
]]]) – A config dictionary that can contain modelspecific options.
 Return type
Optional
[Tensor
] Returns
dtensor of the best point.

cross_validate
(Xs_train, Ys_train, Yvars_train, X_test)[source]¶ Do cross validation with the given training and test sets.
Training set is given in the same format as to fit. Test set is given in the same format as to predict.
 Parameters
Xs_train (
List
[Tensor
]) – A list of m (k_i x d) feature tensors X. Number of rows k_i can vary from i=1,…,m.Ys_train (
List
[Tensor
]) – The corresponding list of m (k_i x 1) outcome tensors Y, for each outcome.Yvars_train (
List
[Tensor
]) – The variances of each entry in Ys, same shape.X_test (
Tensor
) – (j x d) tensor of the j points at which to make predictions.
 Return type
Tuple
[Tensor
,Tensor
] Returns
2element tuple containing
(j x m) tensor of outcome predictions at X.
(j x m x m) tensor of predictive covariances at X. cov[j, m1, m2] is Cov[m1@j, m2@j].

fit
(Xs, Ys, Yvars, bounds, task_features, feature_names, fidelity_features)[source]¶ Fit model to m outcomes.
 Parameters
Xs (
List
[Tensor
]) – A list of m (k_i x d) feature tensors X. Number of rows k_i can vary from i=1,…,m.Ys (
List
[Tensor
]) – The corresponding list of m (k_i x 1) outcome tensors Y, for each outcome.Yvars (
List
[Tensor
]) – The variances of each entry in Ys, same shape.bounds (
List
[Tuple
[float
,float
]]) – A list of d (lower, upper) tuples for each column of X.task_features (
List
[int
]) – Columns of X that take integer values and should be treated as task parameters.fidelity_features (
List
[int
]) – Columns of X that should be treated as fidelity parameters.
 Return type
None

gen
(n, bounds, objective_weights, outcome_constraints=None, linear_constraints=None, fixed_features=None, pending_observations=None, model_gen_options=None, rounding_func=None)[source]¶ Generate new candidates.
 Parameters
n (
int
) – Number of candidates to generate.bounds (
List
[Tuple
[float
,float
]]) – A list of (lower, upper) tuples for each column of X.objective_weights (
Tensor
) – The objective is to maximize a weighted sum of the columns of f(x). These are the weights.outcome_constraints (
Optional
[Tuple
[Tensor
,Tensor
]]) – A tuple of (A, b). For k outcome constraints and m outputs at f(x), A is (k x m) and b is (k x 1) such that A f(x) <= b.linear_constraints (
Optional
[Tuple
[Tensor
,Tensor
]]) – A tuple of (A, b). For k linear constraints on ddimensional x, A is (k x d) and b is (k x 1) such that A x <= b.fixed_features (
Optional
[Dict
[int
,float
]]) – A map {feature_index: value} for features that should be fixed to a particular value during generation.pending_observations (
Optional
[List
[Tensor
]]) – A list of m (k_i x d) feature tensors X for m outcomes and k_i pending observations for outcome i.model_gen_options (
Optional
[Dict
[str
,Union
[int
,float
,str
,AcquisitionFunction
]]]) – A config dictionary that can contain modelspecific options.
 Return type
Tuple
[Tensor
,Tensor
] Returns
2element tuple containing
(n x d) tensor of generated points.
ntensor of weights for each point.

predict
(X)[source]¶ Predict
 Parameters
X (
Tensor
) – (j x d) tensor of the j points at which to make predictions. Return type
Tuple
[Tensor
,Tensor
] Returns
2element tuple containing
(j x m) tensor of outcome predictions at X.
(j x m x m) tensor of predictive covariances at X. cov[j, m1, m2] is Cov[m1@j, m2@j].

Discrete Models¶
ax.models.discrete.eb_thompson module¶

class
ax.models.discrete.eb_thompson.
EmpiricalBayesThompsonSampler
(num_samples=10000, min_weight=None, uniform_weights=False)[source]¶ Bases:
ax.models.discrete.thompson.ThompsonSampler
Generator for Thompson sampling using Empirical Bayes estimates.
The generator applies positivepart JamesStein Estimator to the data passed in via fit and then performs Thompson Sampling.
ax.models.discrete.full_factorial module¶

class
ax.models.discrete.full_factorial.
FullFactorialGenerator
(max_cardinality=100, check_cardinality=True)[source]¶ Bases:
ax.models.discrete_base.DiscreteModel
Generator for full factorial designs.
Generates arms for all possible combinations of parameter values, each with weight 1.
The value of n supplied to gen will be ignored, as the number of arms generated is determined by the list of parameter values. To suppress this warning, use n = 1.

gen
(n, parameter_values, objective_weights, outcome_constraints=None, fixed_features=None, pending_observations=None, model_gen_options=None)[source]¶ Generate new candidates.
 Parameters
n (
int
) – Number of candidates to generate.parameter_values (
List
[List
[Union
[str
,float
,int
,None
]]]) – A list of possible values for each parameter.objective_weights (
Optional
[ndarray
]) – The objective is to maximize a weighted sum of the columns of f(x). These are the weights.outcome_constraints (
Optional
[Tuple
[ndarray
,ndarray
]]) – A tuple of (A, b). For k outcome constraints and m outputs at f(x), A is (k x m) and b is (k x 1) such that A f(x) <= b.fixed_features (
Optional
[Dict
[int
,Union
[str
,float
,int
,None
]]]) – A map {feature_index: value} for features that should be fixed to a particular value during generation.pending_observations (
Optional
[List
[List
[List
[Union
[str
,float
,int
,None
]]]]]) – A list of m lists of parameterizations (each parameterization is a list of parameter values of length d), each of length k_i, for each outcome i.model_gen_options (
Optional
[Dict
[str
,Union
[int
,float
,str
,AcquisitionFunction
]]]) – A config dictionary that can contain modelspecific options.
 Return type
Tuple
[List
[List
[Union
[str
,float
,int
,None
]]],List
[float
]] Returns
2element tuple containing
List of n generated points, where each point is represented by a list of parameter values.
List of weights for each of the n points.

ax.models.discrete.thompson module¶

class
ax.models.discrete.thompson.
ThompsonSampler
(num_samples=10000, min_weight=None, uniform_weights=False)[source]¶ Bases:
ax.models.discrete_base.DiscreteModel
Generator for Thompson sampling.
The generator performs Thompson sampling on the data passed in via fit. Arms are given weight proportional to the probability that they are winners, according to Monte Carlo simulations.

fit
(Xs, Ys, Yvars, parameter_values, outcome_names)[source]¶ Fit model to m outcomes.
 Parameters
Xs (
List
[List
[List
[Union
[str
,float
,int
,None
]]]]) – A list of m lists X of parameterizations (each parameterization is a list of parameter values of length d), each of length k_i, for each outcome.Ys (
List
[List
[float
]]) – The corresponding list of m lists Y, each of length k_i, for each outcome.Yvars (
List
[List
[float
]]) – The variances of each entry in Ys, same shape.parameter_values (
List
[List
[Union
[str
,float
,int
,None
]]]) – A list of possible values for each parameter.
 Return type
None

gen
(n, parameter_values, objective_weights, outcome_constraints=None, fixed_features=None, pending_observations=None, model_gen_options=None)[source]¶ Generate new candidates.
 Parameters
n (
int
) – Number of candidates to generate.parameter_values (
List
[List
[Union
[str
,float
,int
,None
]]]) – A list of possible values for each parameter.objective_weights (
Optional
[ndarray
]) – The objective is to maximize a weighted sum of the columns of f(x). These are the weights.outcome_constraints (
Optional
[Tuple
[ndarray
,ndarray
]]) – A tuple of (A, b). For k outcome constraints and m outputs at f(x), A is (k x m) and b is (k x 1) such that A f(x) <= b.fixed_features (
Optional
[Dict
[int
,Union
[str
,float
,int
,None
]]]) – A map {feature_index: value} for features that should be fixed to a particular value during generation.pending_observations (
Optional
[List
[List
[List
[Union
[str
,float
,int
,None
]]]]]) – A list of m lists of parameterizations (each parameterization is a list of parameter values of length d), each of length k_i, for each outcome i.model_gen_options (
Optional
[Dict
[str
,Union
[int
,float
,str
,AcquisitionFunction
]]]) – A config dictionary that can contain modelspecific options.
 Return type
Tuple
[List
[List
[Union
[str
,float
,int
,None
]]],List
[float
]] Returns
2element tuple containing
List of n generated points, where each point is represented by a list of parameter values.
List of weights for each of the n points.

predict
(X)[source]¶ Predict
 Parameters
X (
List
[List
[Union
[str
,float
,int
,None
]]]) – List of the j parameterizations at which to make predictions. Return type
Tuple
[ndarray
,ndarray
] Returns
2element tuple containing
(j x m) array of outcome predictions at X.
(j x m x m) array of predictive covariances at X. cov[j, m1, m2] is Cov[m1@j, m2@j].

NumPy Models¶
ax.models.numpy.randomforest module¶

class
ax.models.numpy.randomforest.
RandomForest
(max_features='sqrt', num_trees=500)[source]¶ Bases:
ax.models.numpy_base.NumpyModel
A Random Forest model.
Uses a parametric bootstrap to handle uncertainty in Y.
Can be used to fit data, make predictions, and do cross validation; however gen is not implemented and so this model cannot generate new points.
 Parameters

cross_validate
(Xs_train, Ys_train, Yvars_train, X_test)[source]¶ Do cross validation with the given training and test sets.
Training set is given in the same format as to fit. Test set is given in the same format as to predict.
 Parameters
Xs_train (
List
[ndarray
]) – A list of m (k_i x d) feature matrices X. Number of rows k_i can vary from i=1,…,m.Ys_train (
List
[ndarray
]) – The corresponding list of m (k_i x 1) outcome arrays Y, for each outcome.Yvars_train (
List
[ndarray
]) – The variances of each entry in Ys, same shape.X_test (
ndarray
) – (j x d) array of the j points at which to make predictions.
 Return type
Tuple
[ndarray
,ndarray
] Returns
2element tuple containing
(j x m) array of outcome predictions at X.
(j x m x m) array of predictive covariances at X. cov[j, m1, m2] is Cov[m1@j, m2@j].

fit
(Xs, Ys, Yvars, bounds, task_features, feature_names, fidelity_features)[source]¶ Fit model to m outcomes.
 Parameters
Xs (
List
[ndarray
]) – A list of m (k_i x d) feature matrices X. Number of rows k_i can vary from i=1,…,m.Ys (
List
[ndarray
]) – The corresponding list of m (k_i x 1) outcome arrays Y, for each outcome.Yvars (
List
[ndarray
]) – The variances of each entry in Ys, same shape.bounds (
List
[Tuple
[float
,float
]]) – A list of d (lower, upper) tuples for each column of X.task_features (
List
[int
]) – Columns of X that take integer values and should be treated as task parameters.fidelity_features (
List
[int
]) – Columns of X that should be treated as fidelity parameters.
 Return type
None

predict
(X)[source]¶ Predict
 Parameters
X (
ndarray
) – (j x d) array of the j points at which to make predictions. Return type
Tuple
[ndarray
,ndarray
] Returns
2element tuple containing
(j x m) array of outcome predictions at X.
(j x m x m) array of predictive covariances at X. cov[j, m1, m2] is Cov[m1@j, m2@j].
Random Models¶
ax.models.random.base module¶

class
ax.models.random.base.
RandomModel
(deduplicate=False, seed=None)[source]¶ Bases:
ax.models.base.Model
This class specifies the basic skeleton for a random model.
As random generators do not make use of models, they do not implement the fit or predict methods.
These models do not need data, or optimization configs.
To satisfy search space parameter constraints, these models can use rejection sampling. To enable rejection sampling for a subclass, only only _gen_samples needs to be implemented, or alternatively, _gen_unconstrained/gen can be directly implemented.

deduplicate
¶ If specified, a single instantiation of the model will not return the same point twice. This flag is used in rejection sampling.

scramble
¶ If True, permutes the parameter values among the elements of the Sobol sequence. Default is True.

seed
¶ An optional seed value for scrambling.

gen
(n, bounds, linear_constraints=None, fixed_features=None, model_gen_options=None, rounding_func=None)[source]¶ Generate new candidates.
 Parameters
n (
int
) – Number of candidates to generate.bounds (
List
[Tuple
[float
,float
]]) – A list of (lower, upper) tuples for each column of X. Defined on [0, 1]^d.linear_constraints (
Optional
[Tuple
[ndarray
,ndarray
]]) – A tuple of (A, b). For k linear constraints on ddimensional x, A is (k x d) and b is (k x 1) such that A x <= b.fixed_features (
Optional
[Dict
[int
,float
]]) – A map {feature_index: value} for features that should be fixed to a particular value during generation.model_gen_options (
Optional
[Dict
[str
,Union
[int
,float
,str
,AcquisitionFunction
]]]) – A config dictionary that is passed along to the model.rounding_func (
Optional
[Callable
[[ndarray
],ndarray
]]) – A function that rounds an optimization result appropriately (e.g., according to roundtrip transformations).
 Return type
Tuple
[ndarray
,ndarray
] Returns
2element tuple containing
(n x d) array of generated points.
Uniform weights, an narray of ones for each point.

ax.models.random.sobol module¶

class
ax.models.random.sobol.
SobolGenerator
(seed=None, deduplicate=False, init_position=0, scramble=True)[source]¶ Bases:
ax.models.random.base.RandomModel
This class specifies the generation algorithm for a Sobol generator.
As Sobol does not make use of a model, it does not implement the fit or predict methods.

deduplicate
¶ If true, a single instantiation of the generator will not return the same point twice.

init_position
¶ The initial state of the Sobol generator. Starts at 0 by default.

scramble
¶ If True, permutes the parameter values among the elements of the Sobol sequence. Default is True.

seed
¶ An optional seed value for scrambling.

gen
(n, bounds, linear_constraints=None, fixed_features=None, model_gen_options=None, rounding_func=None)[source]¶ Generate new candidates.
 Parameters
n (
int
) – Number of candidates to generate.bounds (
List
[Tuple
[float
,float
]]) – A list of (lower, upper) tuples for each column of X.linear_constraints (
Optional
[Tuple
[ndarray
,ndarray
]]) – A tuple of (A, b). For k linear constraints on ddimensional x, A is (k x d) and b is (k x 1) such that A x <= b.fixed_features (
Optional
[Dict
[int
,float
]]) – A map {feature_index: value} for features that should be fixed to a particular value during generation.rounding_func (
Optional
[Callable
[[ndarray
],ndarray
]]) – A function that rounds an optimization result appropriately (e.g., according to roundtrip transformations) but unused here.
 Return type
Tuple
[ndarray
,ndarray
] Returns
2element tuple containing
(n x d) array of generated points.
Uniform weights, an narray of ones for each point.

ax.models.random.uniform module¶

class
ax.models.random.uniform.
UniformGenerator
(deduplicate=False, seed=None)[source]¶ Bases:
ax.models.random.base.RandomModel
This class specifies a uniform random generation algorithm.
As a uniform generator does not make use of a model, it does not implement the fit or predict methods.

seed
¶ An optional seed value for the underlying PRNG.

Torch Models¶
ax.models.torch.botorch module¶

class
ax.models.torch.botorch.
BotorchModel
(model_constructor=<function get_and_fit_model>, model_predictor=<function predict_from_model>, acqf_constructor=<function get_NEI>, acqf_optimizer=<function scipy_optimizer>, refit_on_cv=False, refit_on_update=True, warm_start_refitting=True, **kwargs)[source]¶ Bases:
ax.models.torch_base.TorchModel
Customizable botorch model.
By default, this uses a noisy Expected Improvement acquisition funciton on top of a model made up of separate GPs, one for each outcome. This behavior can be modified by providing custom implementations of the following components:
a model_constructor that instantiates and fits a model on data
a model_predictor that predicts using the fitted model
a acqf_constructor that creates an acquisition function from a fitted model
a acqf_optimizer that optimizes the acquisition function
 Parameters
model_constructor (
Callable
[[List
[Tensor
],List
[Tensor
],List
[Tensor
],List
[int
],Optional
[Dict
[str
,Tensor
]],Any
],Model
]) – A callable that instantiates and fits a model on data, with signature as described below.model_predictor (
Callable
[[Model
,Tensor
],Tuple
[Tensor
,Tensor
]]) – A callable that predicts using the fitted model, with signature as described below.acqf_constructor (
Callable
[[Model
,Tensor
,Optional
[Tuple
[Tensor
,Tensor
]],Optional
[Tensor
],Optional
[Tensor
],Any
],AcquisitionFunction
]) – A callable that creates an acquisition function from a fitted model, with signature as described below.acqf_optimizer (
Callable
[[AcquisitionFunction
,Tensor
,int
,Optional
[List
[Tuple
[Tensor
,Tensor
,float
]]],Optional
[Dict
[int
,float
]],Optional
[Callable
[[Tensor
],Tensor
]],Any
],Tensor
]) – A callable that optimizes the acquisition function, with signature as described below.refit_on_cv (
bool
) – If True, refit the model for each fold when performing crossvalidation.
Call signatures:
model_constructor( Xs, Ys, Yvars, task_features, state_dict, fidelity_features, **kwargs ) > model
Here Xs, Ys, Yvars are lists of tensors (one element per outcome), task_features identifies columns of Xs that should be modeled as a task, state_dict is a pytorch module state dict, ‘fidelity_features’ is a list of ints that specify the positions of fidelity parameters in ‘Xs’, and model is a botorch Model. Optional kwargs are being passed through from the BotorchModel constructor. This callable is assumed to return a fitted botorch model that has the same dtype and lives on the same device as the input tensors.
model_predictor(model, X) > [mean, cov]
Here model is a fitted botorch model, X is a tensor of candidate points, and mean and cov are the posterior mean and covariance, respectively.
acqf_constructor( model, objective_weights, outcome_constraints, X_observed, X_pending, **kwargs, ) > acq_function
Here model is a botorch Model, objective_weights is a tensor of weights for the model outputs, outcome_constraints is a tuple of tensors describing the (linear) outcome constraints, X_observed are previously observed points, and X_pending are points whose evaluation is pending. acq_function is a botorch acquisition function crafted from these inputs. For additional details on the arguments, see get_NEI.
acqf_optimizer( acq_function, bounds, n, inequality_constraints, fixed_features, rounding_func, **kwargs, ) > candidates
Here acq_function is a BoTorch AcquisitionFunction, bounds is a tensor containing bounds on the parameters, n is the number of candidates to be generated, inequality_constraints are inequality constraints on parameter values, fixed_features specifies features that should be fixed during generation, and rounding_func is a callback that rounds an optimization result appropriately. candidates is a tensor of generated candidates. For additional details on the arguments, see scipy_optimizer.

best_point
(bounds, objective_weights, outcome_constraints=None, linear_constraints=None, fixed_features=None, model_gen_options=None)[source]¶ Identify the current best point, satisfying the constraints in the same format as to gen.
Return None if no such point can be identified.
 Parameters
bounds (
List
[Tuple
[float
,float
]]) – A list of (lower, upper) tuples for each column of X.objective_weights (
Tensor
) – The objective is to maximize a weighted sum of the columns of f(x). These are the weights.outcome_constraints (
Optional
[Tuple
[Tensor
,Tensor
]]) – A tuple of (A, b). For k outcome constraints and m outputs at f(x), A is (k x m) and b is (k x 1) such that A f(x) <= b.linear_constraints (
Optional
[Tuple
[Tensor
,Tensor
]]) – A tuple of (A, b). For k linear constraints on ddimensional x, A is (k x d) and b is (k x 1) such that A x <= b.fixed_features (
Optional
[Dict
[int
,float
]]) – A map {feature_index: value} for features that should be fixed to a particular value in the best point.model_gen_options (
Optional
[Dict
[str
,Union
[int
,float
,str
,AcquisitionFunction
]]]) – A config dictionary that can contain modelspecific options.
 Return type
Optional
[Tensor
] Returns
dtensor of the best point.

cross_validate
(Xs_train, Ys_train, Yvars_train, X_test)[source]¶ Do cross validation with the given training and test sets.
Training set is given in the same format as to fit. Test set is given in the same format as to predict.
 Parameters
Xs_train (
List
[Tensor
]) – A list of m (k_i x d) feature tensors X. Number of rows k_i can vary from i=1,…,m.Ys_train (
List
[Tensor
]) – The corresponding list of m (k_i x 1) outcome tensors Y, for each outcome.Yvars_train (
List
[Tensor
]) – The variances of each entry in Ys, same shape.X_test (
Tensor
) – (j x d) tensor of the j points at which to make predictions.
 Return type
Tuple
[Tensor
,Tensor
] Returns
2element tuple containing
(j x m) tensor of outcome predictions at X.
(j x m x m) tensor of predictive covariances at X. cov[j, m1, m2] is Cov[m1@j, m2@j].

fit
(Xs, Ys, Yvars, bounds, task_features, feature_names, fidelity_features)[source]¶ Fit model to m outcomes.
 Parameters
Xs (
List
[Tensor
]) – A list of m (k_i x d) feature tensors X. Number of rows k_i can vary from i=1,…,m.Ys (
List
[Tensor
]) – The corresponding list of m (k_i x 1) outcome tensors Y, for each outcome.Yvars (
List
[Tensor
]) – The variances of each entry in Ys, same shape.bounds (
List
[Tuple
[float
,float
]]) – A list of d (lower, upper) tuples for each column of X.task_features (
List
[int
]) – Columns of X that take integer values and should be treated as task parameters.fidelity_features (
List
[int
]) – Columns of X that should be treated as fidelity parameters.
 Return type
None

gen
(n, bounds, objective_weights, outcome_constraints=None, linear_constraints=None, fixed_features=None, pending_observations=None, model_gen_options=None, rounding_func=None)[source]¶ Generate new candidates.
An initialized acquisition function can be passed in as model_gen_options[“acquisition_function”].
 Parameters
n (
int
) – Number of candidates to generate.bounds (
List
[Tuple
[float
,float
]]) – A list of (lower, upper) tuples for each column of X.objective_weights (
Tensor
) – The objective is to maximize a weighted sum of the columns of f(x). These are the weights.outcome_constraints (
Optional
[Tuple
[Tensor
,Tensor
]]) – A tuple of (A, b). For k outcome constraints and m outputs at f(x), A is (k x m) and b is (k x 1) such that A f(x) <= b. (Not used by single task models)linear_constraints (
Optional
[Tuple
[Tensor
,Tensor
]]) – A tuple of (A, b). For k linear constraints on ddimensional x, A is (k x d) and b is (k x 1) such that A x <= b.fixed_features (
Optional
[Dict
[int
,float
]]) – A map {feature_index: value} for features that should be fixed to a particular value during generation.pending_observations (
Optional
[List
[Tensor
]]) – A list of m (k_i x d) feature tensors X for m outcomes and k_i pending observations for outcome i.model_gen_options (
Optional
[Dict
[str
,Union
[int
,float
,str
,AcquisitionFunction
]]]) – A config dictionary that can contain modelspecific options.rounding_func (
Optional
[Callable
[[Tensor
],Tensor
]]) – A function that rounds an optimization result appropriately (i.e., according to roundtrip transformations).
 Returns
n x ddim Tensor of generated points. Tensor: ndim Tensor of weights for each point.
 Return type
Tensor

predict
(X)[source]¶ Predict
 Parameters
X (
Tensor
) – (j x d) tensor of the j points at which to make predictions. Return type
Tuple
[Tensor
,Tensor
] Returns
2element tuple containing
(j x m) tensor of outcome predictions at X.
(j x m x m) tensor of predictive covariances at X. cov[j, m1, m2] is Cov[m1@j, m2@j].