tfp.experimental.bayesopt.acquisition.WeightedPowerScalarization

Weighted power scalarization acquisition function.

Inherits From: AcquisitionFunction

tfp.experimental.bayesopt.acquisition.WeightedPowerScalarization(
    predictive_distribution,
    observations,
    seed=None,
    acquisition_function_classes=None,
    acquisition_kwargs_list=None,
    power=None,
    weights=None
)

Given a multi-task distribution over T tasks, the weighted power scalarization acquisition function computes

(sum_t w_t |a_t(x)|^p)^(1/p)

where:

  • a_t are the list of acquisition_function_classes.
  • w_t are weights.
  • p is power.

By default p is None which corresponds to a value of inf. This is Chebyshev scalarization: max w_t |a_t(x)|, and for non inf p corresponds to weighted power scalarization.

Examples

Build and evaluate a Weighted Power Scalarization acquisition function.

import numpy as np
import tensorflow_probability as tfp

tfpk = tfp.math.psd_kernels
tfpke = tfp.experimental.psd_kernels
tfde = tfp.experimental.distributions
tfp_acq = tfp.experimental.bayesopt.acquisition

kernel = tfpk.ExponentiatedQuadratic()
mt_kernel = tfpke.Independent(base_kernel=kernel, num_tasks=4)

# Sample 10 20-dimensional index points and associated 4-dimensional
# observations.
index_points = np.random.uniform(size=[10, 20])
observations = np.random.uniform(size=[10, 4])

# Build a multitask GP.
dist = tfde.MultiTaskGaussianProcessRegressionModel(
    kernel=mt_kernel,
    observation_index_points=index_points,
    observations,
    observation_noise_variance=1e-4)

# Choose weights and acquisition functions for each task.
weights = np.array([0.8, 1., 1.1, 0.5])
acquisition_function_classes = [
    tfp_acq.GaussianProcessExpectedImprovement,
    tfp_acq.GaussianProcessUpperConfidenceBound,
    tfp_acq.GaussianProcessExpectedImprovement,
    tfp_acq.GaussianProcessUpperConfidenceBound]

# Build the acquisition function.
cheb_scalar_fn = tfp_acq.WeightedPowerScalarization(
    predictive_distribution=dist,
    acquisition_function_classes=acquisition_function_classes,
    observations=observations,
    weights=weights)

# Evaluate the acquisition function on 6 predictive index points. Note that
# `index_points` must be passed as a keyword arg.
pred_index_points = np.random.uniform(size=[6, 20])
acq_fn_vals = cheb_scalar_fn(index_points=pred_index_points)

predictive_distribution tfd.Distribution-like, the distribution over observations at a set of index points (expected to be a tfd.MultiTaskGaussianProcess or tfd.MultiTaskGaussianProcessRegressionModel).
observations Float Tensor of observed function values. Shape has the form [b1, ..., bB, N, T], where N is the number of index points and T is the number of tasks (such that the event shape of predictive_distribution is [N, T]) and [b1, ..., bB] is broadcastable with the batch shape of predictive_distribution.
seed PRNG seed; see tfp.random.sanitize_seed for details.
acquisition_function_classes Callable acquisition function, one per task.
acquisition_kwargs_list Kwargs to pass in to acquisition function.
power Numpy float. When this is set to None, this corresponds to Chebyshev scalarization.
weights Tensor of shape [T] where, T is the number of tasks.

acquisition_function_classes

acquisition_kwargs_list

is_parallel Python bool indicating whether the acquisition function is parallel.

Parallel (batched) acquisition functions evaluate batches of points rather than single points.

observations Float Tensor of observations.
power

predictive_distribution The distribution over observations at a set of index points.
seed PRNG seed.
weights

Methods

__call__

View source

__call__(
    **kwargs
)

Computes the weighted power scalarization.

Args
**kwargs Keyword args passed on to the mean and stddev methods of predictive_distribution.

Returns
Weighted power scalarization at index points implied by predictive_distribution (or overridden in **kwargs).