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Noisy function evaluation

As explained in Bayesian Optimization in Action

A noisy observation is an observed label or function value corrupted by stochastic or measurement noise.

A noisy function evaluation occurs when an observed label or function value is corrupted by stochastic or measurement noise. In Gaussian-process modeling, the noise level can be specified explicitly, so predictive uncertainty at observed points remains above zero rather than collapsing completely. section 1.2.1

The distinction matters because an observed value may not reveal the exact underlying function value. A Gaussian process represents that uncertainty with predictive confidence intervals, allowing decisions to account for both expected performance and reliability. section 1.2.1

Noisy evaluations change Bayesian optimization in several practical ways:

  • Keep uncertainty at training locations at the specified noise level instead of treating every observation as exact. section 1.2.1
  • Prefer acquisition policies designed for noisy predictions when selecting the next evaluation. section 10.4
  • Compare candidates using uncertainty as well as their predicted means, especially when decisions are high-risk or evaluations are expensive. section 1.2.1

Choosing a neural-network depth

Suppose a Gaussian process predicts accuracy of 0.85 for both 25 and 15 layers. The 25-layer model has a 95% confidence interval of 0.81–0.89, while the 15-layer model has an interval of 0.84–0.86. The narrower interval makes 15 layers the more dependable choice, even though both have the same predicted mean. section 1.2.1

policy = qNoisyExpectedImprovement(model, train_x)  #1
 
challenger, acq_val = optimize_acqf(                #2
    policy,                                         #2
    bounds=bounds,                                  #2
    q=1,                                            #2
    num_restarts=50,                                #2
    raw_samples=100,                                #2
)                                                   #2

Use the qNoisyExpectedImprovement listing to see how a noisy acquisition policy is optimized over the search space. section 10.4

How Bayesian Optimization in Action covers it

How deep it goes
Defines noisy labels, specifies GP noise levels, and applies a noise-aware acquisition policy without deriving the underlying noise model.
Examples
Uses neural-network layer selection and preference optimization with a king-of-the-hill challenger strategy.
What it assumes
Assumes basic Gaussian-process and Bayesian-optimization ideas while introducing noisy observations through confidence intervals and examples.
What you can do after
Apply via qNoisyExpectedImprovement when selecting Bayesian-optimization evaluations under uncertain observations.
How it connects
Connects Gaussian processes, uncertainty quantification, Bayesian optimization, confidence intervals, and acquisition functions.
Cover of Bayesian Optimization in Action
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Related concepts

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.