Part 4 of 8

The Maths II: Acquisition Functions

The posterior hands us μ_n(x) and σ_n(x); an acquisition function turns those two numbers into a decision. This section derives the classic by hand, tours the zoo, and covers the two upgrades a modern practitioner actually ships: LogEI and batch acquisition. Throughout, f^*_n = max_i y_i is the best value observed so far and z = (μ_n(x) − f^*_n) / σ_n(x).

1. Improvement, and its expectation
2. The acquisition zoo
3. Numerics and batches: LogEI and qEI
4. The knowledge gradient: valuing what you will believe
5. Paying for the knowledge gradient
6. Quiz: 5 questions