tfp.experimental.bayesopt.acquisition.ParallelUpperConfidenceBound

Parallel upper confidence bound acquisition function.

Inherits From: AcquisitionFunction

tfp.experimental.bayesopt.acquisition.ParallelUpperConfidenceBound(
    predictive_distribution,
    observations,
    seed=None,
    exploration=0.01,
    num_samples=100,
    transform_fn=None
)

Computes the q-UCB based on observed data using a stochastic process surrogate model. The computation is of the form mean + exploration * stddev.

Requires that predictive_distribution has a sample method.

Examples

Build and evaluate a Parallel 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 10 20-dimensional index points and associated observations.
index_points = np.random.uniform(size=[10, 20])
observations = np.random.uniform(size=[10])

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

gp_pucb = tfp_acq.ParallelUpperConfidenceBound(
    predictive_distribution=dist,
    observations=observations,
    exploration=0.05,
    num_samples=int(2e4))

# Evaluate the acquisition function at a set of predictive index points.
pred_index_points = np.random.uniform(size=[6, 20])
acq_fn_vals = gp_pucb(pred_index_points)  # Has shape [6].

predictive_distribution tfd.Distribution-like, the distribution over observations at a set of index points. Must have a sample method.
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.
num_samples The number of samples to use for the Paralle Expected Improvement approximation.
transform_fn Optional Python Callable that transforms objective values. This is used for optimizing a composite grey box function g(f(x)) where f is our black box function and g is transform_fn.

exploration

is_parallel Python bool indicating whether the acquisition function is parallel.

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

num_samples

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

Methods

__call__

View source

__call__(
    **kwargs
)

Computes the Parallel Upper Confidence Bound.

Args
**kwargs Keyword args passed on to the sample method of predictive_distribution.

Returns
Parallel upper confidence bounds at index points implied by predictive_distribution (or overridden in **kwargs).

References

[1] J. Wilson, R. Moriconi, F. Hutter, M. Deisenroth The reparameterization trick for acquisition functions https://bayesopt.github.io/papers/2017/32.pdf