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ProbabilityOfImprovement

As explained in Bayesian Optimization in Action

ProbabilityOfImprovement is a BoTorch acquisition-module class that computes probability-of-improvement scores from a Gaussian process and an incumbent value.

ProbabilityOfImprovement is a BoTorch acquisition-module class for scoring how likely each candidate is to improve on the incumbent, according to a Gaussian-process belief. It favors high predicted means while retaining some interest in uncertain regions. section 4.2.2

BoTorch usage

Create the policy with a GP model and incumbent value, then evaluate a candidate grid: `policy = ProbabilityOfImprovement(model, best_f=train_y.max())`; `scores = policy(xs.unsqueeze(1))`. Optimize those scores with `optimize_acqf`; for the illustrated search, the next point is approximately 0.5985.

How Bayesian Optimization in Action covers it

How deep it goes
Explains GP-based scoring behavior and implementation, then stops short of detailed acquisition-function internals.
Examples
Uses a dense grid from −5 to 5, GP predictive regions, and an optimized next point near 0.5985.
What it assumes
Assumes a trained GP, predictive distributions, and an incumbent value for comparison.
What you can do after
Apply it via BoTorch to score candidates and select the next query by maximizing probability of improvement.
How it connects
Connects Gaussian processes, Bayesian optimization, acquisition functions, and incumbent values.
Cover of Bayesian Optimization in Action
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