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Return on investment

As explained in Bayesian Optimization in Action

A return on investment measure is a ratio of profit or benefit gained from an investment to the cost of making that investment.

Return on investment (ROI) measures profit or benefit per unit of investment cost. In multifidelity optimization, it divides the information gained about an objective's optimum by the cost of querying a data point. section 9.3.2

Use the ROI acquisition score to balance information and expense:

  • Prefer the query with greater information gain when candidate queries cost the same. section 9.3.2
  • Prefer the cheaper query when candidate queries provide the same information. section 9.3.2
  • Use informative low-fidelity queries while they remain valuable, then switch to high-fidelity queries when necessary. section 9.3.2

Choosing a fidelity

A multifidelity MES policy may prefer low-fidelity points when their cost is low and their information gain is useful. It may prefer high-fidelity points when low-fidelity observations are insufficient or nearly as expensive.

How Bayesian Optimization in Action covers it

How deep it goes
Defines the ratio, explains its decision rules, and stops short of deriving the underlying information-gain measure.
Examples
Uses low- versus high-fidelity queries with differing costs and information gains to illustrate switching preferences.
What it assumes
Assumes maximum-value entropy search, acquisition scores, objective optima, and fidelity-dependent query costs.
What you can do after
Apply it via a cost-aware acquisition utility to rank multifidelity queries by information gained per unit cost.
How it connects
Connects return on investment with multifidelity optimization, maximum-value entropy search, acquisition functions, and Bayesian optimization.

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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.