class_docstr: Analytical Gaussian Process upper confidence bound acquisition function.
  
  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.
  
  ```python
  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].
  ```
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docstr: Constructs a GP Upper Confidence Bound acquisition function.
  
  Args:
    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.
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code: def __init__(
      self,
      predictive_distribution,
      observations,
      seed=None,
      exploration=0.01,
  ):
      """Constructs a GP Upper Confidence Bound acquisition function.
  
      Args:
        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.
      """
  
      self._exploration = exploration
      super(GaussianProcessUpperConfidenceBound, self).__init__(
          predictive_distribution=predictive_distribution,
          observations=observations,
          seed=seed,
      )
  
file_path: probability/tensorflow_probability/python/experimental/bayesopt/acquisition/upper_confidence_bound.py
imports: import tensorflow.compat.v2
  from tensorflow_probability.python.experimental.bayesopt.acquisition import acquisition_function
  from tensorflow_probability.python.internal import dtype_util
  from tensorflow_probability.python.internal import samplers
label_desc: Use image node_id 1 to create a new GaussianProcessUpperConfidenceBound object from inherited base classes: acquisition_function with example: obj = GaussianProcessUpperConfidenceBound(predictive_distribution, observations, seed, exploration)