Batch acquisition score

As explained in Bayesian Optimization in Action

A batch acquisition score is a numerical measure of the expected usefulness of evaluating a group of candidate points together.

A batch acquisition score measures how promising a group of candidate evaluations is when they will be queried together. For batch probability of improvement (PoI), it is the probability that the batch's best returned value exceeds the incumbent: Pr(max{f(x₁), …, f(xₖ)} > f*). section 7.2.1

Use the score to:

• Treat the maximum evaluation in the batch as the batch's improvement signal rather than judging candidates independently. section 7.2.1
• Select the batch x₁, …, xₖ that maximizes the acquisition score. section 7.2.1
• Distinguish PoI, which asks whether improvement occurs, from expected improvement, which asks how much improvement occurs. section 7.2.1

Figure 7.5 Extending the mathematical formulation of a BayesOpt policy to the batch setting. In both cases, we use the average of a quantity of interest. In the batch setting, we take the maximum value across the points in a batch before taking the average to represent the utility of the whole batch.

Compare sequential and batch policies by averaging a quantity of interest after taking the batch maximum, which represents the batch's utility. section 7.2.1

How Bayesian Optimization in Action covers it

How deep it goes

Defines batch PoI mathematically and stops short of detailing its implementation, deferring optimization mechanics to BoTorch.

Examples

Uses sequential-versus-batch comparisons, maximum-value diagrams, and the PoI–EI contrast to illustrate batch utility.

What it assumes

Builds from sequential probability of improvement and the incumbent before extending the comparison to a batch maximum.

What you can do after

Apply it via BoTorch's optimize_acqf() to search for the highest-scoring candidate batch.

How it connects

Connects batch PoI with probability of improvement, expected improvement, incumbent values, Gaussian distributions, and Bayesian optimization.

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Related concepts

• optimize_acqfused by · optimize_acqf is a BoTorch function that optimizes an acquisition function to return a high-scoring candidate and its acquisition value.
• acquisition functionkind of · An acquisition function is a scoring rule that ranks candidate evaluations by their expected usefulness for selecting the next sample or experiment.

This explainer was generated by Manning's knowledge graph from the text of Bayesian Optimization in Action. The section links point to the parts of the book it draws on.