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DominatedPartitioning

As explained in Bayesian Optimization in Action

DominatedPartitioning is a BoTorch class that represents the partition of objective space dominated by a set of points.

DominatedPartitioning represents the portion of objective space dominated by collected multiobjective observations. It uses a reference point to bound that region, then partitions it into hyperrectangles whose volumes can be summed as the dominated hypervolume. section 11.2

Computing dominated hypervolume

For two objectives, store the collected labels in train_y with shape n-by-2, initialize DominatedPartitioning with ref_point and train_y, and call compute_hypervolume(). A larger result indicates a more extensive dominated region. section 11.2

How Bayesian Optimization in Action covers it

How deep it goes
Explains reference-point-bounded partitioning and API usage, while deferring low-level algorithm implementation.
Examples
Uses two-objective collected labels and compares exhaustive search, random search, and BayesOpt through hypervolume.
What it assumes
Assumes collected objective labels and a chosen reference point for a multiobjective optimization problem.
What you can do after
Apply it via BoTorch to calculate the dominated hypervolume of collected multiobjective observations.
How it connects
Connects dominated regions with reference points, hypervolume, Pareto frontiers, and multiobjective optimization.
Cover of Bayesian Optimization in Action
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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.