Acquisition Function

Acquisition function is the decision-theoretic component of Bayesian optimization that converts a probabilistic belief about an unknown objective function into a concrete strategy for choosing the next point to evaluate. It formalizes the exploration-exploitation tradeoff: an acquisition function must balance sampling where the surrogate model predicts high values (exploitation) against sampling where the model is uncertain (exploration). Common choices include Expected Improvement, which computes the expected reduction in the best observed value; Probability of Improvement, which targets the likelihood of any improvement; and Upper Confidence Bound, which treats optimization as a multi-armed bandit problem and selects points with high upper confidence limits.

The choice of acquisition function is not merely a technical detail — it encodes a normative stance toward risk, uncertainty, and the value of information. An optimizer using Expected Improvement is impatient: it prioritizes probable gains over information that might enable larger gains later. An optimizer using Expected Improvement with a high exploration parameter, or one using Information-based acquisition functions, is more patient: it samples to reduce global uncertainty even when immediate improvement is unlikely. This makes the acquisition function a microcosm of decision theory applied to experimental design.