What is Acquisition Function?
An Acquisition Function is a comparatively cheap decision rule that assigns utility to one or more candidate evaluations from a surrogate posterior so a sequential optimizer can choose what to evaluate next.
Quick Facts
| Specification | Official Specification |
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How It Works
Turn posterior beliefs into a decision-specific utility
For a candidate set X, a policy can be written as an expectation of a utility under the current posterior over f(X). BoTorch's acquisition documentation distinguishes analytic single-point functions from Monte Carlo estimators for joint batches. EI rewards expected positive improvement, PI rewards the chance of crossing an incumbent, UCB adds an uncertainty bonus, and information-based methods value reduction in decision-relevant uncertainty.
Treat acquisition optimization as a real numerical problem
Selecting the next point requires optimizing the acquisition function over bounds and constraints. This secondary objective can be non-convex, flat, discontinuous for mixed spaces, or stochastic under Monte Carlo estimation. Use multiple starts, constrained optimizers, stable transformations, fixed random base samples where appropriate, and direct checks against a dense or random candidate set. A high acquisition value found by a weak optimizer does not prove that the global acquisition maximum was found.
Preserve the semantics of noise, batches, cost, and feasibility
A batch utility should account for joint posterior correlation rather than selecting the same single-point maximizer repeatedly. Pending evaluations must be represented in asynchronous systems. Noisy objectives require uncertainty about the latent incumbent, constraints require a declared feasibility treatment, and varying costs require utility per resource or another explicit objective. The Ax introduction shows that EI, PI, and UCB lead to different behavior and have constrained, noisy, multi-objective, and batch extensions.
Key Characteristics
- Maps a posterior distribution to candidate decision utility
- Is cheap relative to the expensive objective but still needs optimization
- Encodes a specific exploration, exploitation, or information trade-off
- Can score single points or correlated batches
- Must represent noise, constraints, pending work, and cost consistently
- Requires policy ablations and end-to-end objective evaluation
Common Use Cases
- Choosing the next point in Bayesian Optimization
- Selecting a diverse batch for parallel experiments
- Prioritizing feasible candidates under black-box constraints
- Allocating evaluations across different fidelity or cost levels
- Choosing informative labels or measurements in sequential learning
Example
Loading code...Frequently Asked Questions
Is an Acquisition Function the same as the objective function?
No. The objective is the expensive quantity the system ultimately wants to optimize. The acquisition function is a cheap, model-based utility used to decide where to evaluate that objective next. Optimizing the acquisition does not itself produce a real objective observation.
Which Acquisition Function should I use?
Start from the decision contract. EI is a strong baseline for improvement under a suitable posterior; UCB exposes an exploration parameter; posterior sampling supports randomized selection; information-based policies suit learning objectives. Test alternatives with the same initialization and total cost.
Why must an Acquisition Function be optimized?
Continuous search spaces contain infinitely many candidates, so the next evaluation is the maximizer of a secondary, usually non-convex function. Multi-start numerical optimization, constraints, mixed variables, Monte Carlo error, and flat gradients can all change the selected point.
How are batch Acquisition Functions different from top-k scores?
Top-k single-point scores ignore correlation and can select redundant candidates. A joint batch policy values the set under the joint posterior or uses an explicit diversity approximation. The system must also account for evaluations that are already pending.
Can an Acquisition Function fix a misspecified surrogate?
No. It makes decisions from the posterior it receives. If the kernel, likelihood, features, noise, or constraints are wrong, a sophisticated policy can confidently spend budget in the wrong region. Validate the surrogate and retain model-free baselines.