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Batch upper confidence bound

As explained in Bayesian Optimization in Action

Batch upper confidence bound is a batch Bayesian optimization acquisition policy that scores multiple candidates using predictive means and uncertainty.

Batch upper confidence bound (UCB) is a Bayesian optimization policy for choosing several objective evaluations in parallel. It scores candidate batches from a Gaussian-process model’s predictions, balancing promising values with uncertainty. section 7.2.2

A batch UCB iteration follows the standard optimization loop with small batch-specific changes:

  • Fit the Gaussian-process model to the accumulated training data. section 7.2.2
  • Construct qUpperConfidenceBound and set beta, such as beta = 2. section 7.2.2
  • Call optimize_acqf with q equal to the batch size; receive a k-by-d tensor of candidates. section 7.2.2
  • Evaluate all candidates, then append their inputs and outputs to the training data. section 7.2.2

Four-query hyperparameter batch

For 20 total queries and a batch size of four, run five iterations. Each iteration optimizes qUpperConfidenceBound, evaluates four SVM hyperparameter settings, and updates the Gaussian-process data. section 7.2.2

policy = botorch.acquisition.monte_carlo.qUpperConfidenceBound(
    model, beta=2
)

Inspect the BoTorch construction of qUpperConfidenceBound with beta = 2. section 7.2.2

How Bayesian Optimization in Action covers it

How deep it goes
Develops the batch loop and implementation changes, but does not provide the UCB mathematical formulation.
Examples
Uses BoTorch code, a two-dimensional toy objective, and SVM tuning with four evaluations per batch.
What it assumes
Assumes a fitted Gaussian-process model and training data, while batch-loop modifications are kept minimal.
What you can do after
Apply it via BoTorch by setting q to the desired batch size and using qUpperConfidenceBound.
How it connects
Connects Bayesian optimization, acquisition functions, Gaussian processes, and hyperparameter tuning.
Cover of Bayesian Optimization in Action
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