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UCB parameter

As explained in Bayesian Optimization in Action

A UCB parameter is a positive scalar that weights predictive uncertainty in an upper confidence bound score and controls its exploration tendency.

The UCB parameter β is a positive scalar in the acquisition score μ + βσ. It weights predictive uncertainty: smaller values favor exploitation near high predicted rewards, while larger values encourage exploration of uncertain regions. section 5.2.3 section 5.5

Choosing β on the Forrester function

With β = 1, UCB may explore too little and remain at a local optimum. Increasing β to 2 supplies enough optimism to find the global optimum, whereas an excessively large value can waste the evaluation budget exploring. section 5.2.3

Useful ways to set the parameter include:

  • Use a fixed value when its exploration tendency suits the objective. section 5.4.2
  • Increase β during optimization with an update such as beta *= multiplier, compensating for shrinking Gaussian-process uncertainty as more data arrive. section 5.4.1
policy = botorch.acquisition.analytic.UpperConfidenceBound(
    model, beta=1
)

Configure β directly in BoTorch’s analytic UpperConfidenceBound policy. section 5.2.3

How Bayesian Optimization in Action covers it

How deep it goes
Defines β in μ + βσ, compares fixed values experimentally, and develops a multiplicative schedule.
Examples
Uses the Forrester function and support-vector-machine hyperparameter tuning to compare fixed and adaptive β values.
What it assumes
Assumes Gaussian-process predictions and Bayesian-optimization loops while grounding β through mean and uncertainty terms.
What you can do after
Apply it via BoTorch by configuring UCB and selecting fixed or scheduled β values for optimization.
How it connects
Connects UCB with Gaussian processes, Bayesian optimization, acquisition functions, and exploration-exploitation trade-offs.
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.