tfp.experimental.bayesopt.acquisition.GaussianProcessUpperConfidenceBound

Analytical Gaussian Process upper confidence bound acquisition function.

Inherits From: AcquisitionFunction

tfp.experimental.bayesopt.acquisition.GaussianProcessUpperConfidenceBound(
    predictive_distribution, observations, seed=None, exploration=0.01
)

Computes the analytic sequential upper confidence bound for a Gaussian process model.

Requires that predictive_distribution has a .mean, stddev method.

Examples

Build and evaluate a GP Upper Confidence Bound acquisition function.

import numpy as np
import tensorflow_probability as tfp

tfd = tfp.distributions
tfpk = tfp.math.psd_kernels
tfp_acq = tfp.experimental.bayesopt.acquisition

# Sample 12 5-dimensional index points and associated observations.
index_points = np.random.uniform(size=[12, 5])
observations = np.random.uniform(size=[12])

# Build a GP regression model conditioned on observed data.
dist = tfd.GaussianProcessRegressionModel(
    kernel=tfpk.ExponentiatedQuadratic(),
    observation_index_points=index_points,
    observations=observations)

# Build a GP upper confidence bound acquisition function.
gp_ucb = tfp_acq.GausianProcessUpperConfidenceBound(
    predictive_distribution=dist,
    observations=observations,
    exploration=0.05,
    num_samples=int(2e4))

# Evaluate the acquisition function at a set of 6 predictive index points.
pred_index_points = np.random.uniform(size=[6, 5])
acq_fn_vals = gp_ucb(pred_index_points)  # Has shape [6].

predictive_distribution tfd.Distribution-like, the distribution over observations at a set of index points. Must have mean, stddev methods.
observations Float Tensor of observations. Shape has the form [b1, ..., bB, e], where e is the number of index points (such that the event shape of predictive_distribution is [e]) and [b1, ..., bB] is broadcastable with the batch shape of predictive_distribution.
seed PRNG seed; see tfp.random.sanitize_seed for details.
exploration Exploitation-exploration trade-off parameter.

exploration

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

Methods

__call__

View source

__call__(
    **kwargs
)

Computes analytic GP upper confidence bound.

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

Returns
Upper confidence bound at index points implied by predictive_distribution (or overridden in **kwargs).