Table of Contents

Enum AcquisitionFunctionType

Namespace
AiDotNet.Enums
Assembly
AiDotNet.dll

Represents different types of acquisition functions used in Bayesian optimization.

public enum AcquisitionFunctionType

Fields

ExpectedImprovement = 1

Expected Improvement acquisition function that focuses on areas likely to improve upon the current best solution.

For Beginners: Expected Improvement (EI) is like a strategic explorer who asks: "Where am I most likely to find something better than the best I've seen so far?"

EI works by:

  1. Keeping track of the best solution found so far
  2. For each unexplored point, calculating how much better it might be than the current best
  3. Weighting this potential improvement by the probability of achieving it
  4. Selecting the point with the highest expected improvement

Key characteristics:

  • Naturally balances exploration and exploitation without extra parameters
  • Focuses more on exploitation as it finds good solutions
  • Tends to explore more efficiently than UCB in many cases
  • Works well when you want to find the very best solution
  • Popular in practical applications like hyperparameter tuning

EI is often the default choice for many Bayesian optimization problems because it efficiently finds good solutions with relatively few evaluations.

ProbabilityOfImprovement = 2

Probability of Improvement acquisition function that maximizes the probability of finding better solutions.

For Beginners: Probability of Improvement (PI) is like a cautious explorer who asks: "What's the chance that this location is better than the best I've found so far?"

PI works by:

  1. Keeping track of the best solution found so far
  2. For each unexplored point, calculating the probability that it's better than the current best
  3. Selecting the point with the highest probability of improvement

Key characteristics:

  • Simpler than Expected Improvement (focuses on probability, not magnitude)
  • Very exploitation-focused once good solutions are found
  • Tends to be more conservative than EI or UCB
  • Good when you want high confidence of improvement
  • May explore less than other methods

PI is useful when you want to be confident that each new evaluation will be better than what you've already found, even if the improvement is small.

UpperConfidenceBound = 0

Upper Confidence Bound acquisition function that balances exploration and exploitation.

For Beginners: The Upper Confidence Bound (UCB) approach is like an optimistic explorer who follows this rule: "I'll check places that either look promising or that I'm very uncertain about."

UCB works by:

  1. Calculating the predicted value at each possible point (exploitation)
  2. Adding an "uncertainty bonus" that's larger for less-explored areas (exploration)
  3. Selecting the point with the highest combined score

The formula is essentially: UCB = predicted_value + exploration_weight × uncertainty

Key characteristics:

  • Has a tunable parameter that controls the exploration-exploitation balance
  • More exploration-focused than some other methods
  • Works well when you want to avoid bad outcomes
  • Simple to understand and implement
  • Provides theoretical guarantees about finding the optimal solution

UCB is particularly useful when you want to be cautious and thoroughly explore the space before committing to a solution.

Remarks

For Beginners: Acquisition functions help an AI system decide where to look next when searching for the best solution to a problem.

Imagine you're trying to find the highest point in a mountain range that's covered in fog:

  • You've already explored a few spots and know their heights
  • Based on these measurements, you can make educated guesses about unexplored areas
  • But you need to decide: should you explore areas that look promising based on what you know so far, or should you check completely unexplored areas that might contain surprises?

This is the "exploration vs. exploitation" trade-off, and acquisition functions help balance it.

Acquisition functions are particularly useful when:

  • Testing each possible solution is expensive or time-consuming
  • You want to find the best solution with as few attempts as possible
  • The relationship between inputs and outputs is complex

Common applications include hyperparameter tuning in machine learning, experimental design, and optimizing complex systems where each test is costly.

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