Bayesian optimization acquisition function selection

bayesian-optimization-acquisition-function-selection

Summary

Select and apply an acquisition function to a fitted Gaussian Process model to propose the next LC gradient point for evaluation in a Bayesian optimization loop. This skill determines whether to favor exploration, exploitation, or a balanced trade-off when navigating the gradient parameter space.

When to use

After fitting a Gaussian Process regression model to prior LC-MS gradient evaluations (where gradients are encoded as input and separation efficiency is output), use this skill to decide which candidate gradient to test next. Apply it when you have ≤10 total allowed runs and need to efficiently allocate remaining trials to improve separation efficiency.

When NOT to use

• If the Gaussian Process model has not yet been fitted to any prior gradient evaluations (no training data available); acquisition function selection requires a trained model.
• If the search space (gridX) is empty or does not cover the relevant gradient parameter bounds; the function cannot propose a meaningful gradient.
• If separation efficiency has already converged or plateaued across multiple consecutive runs; further Bayesian optimization acquisitions will not yield improvement and budget should be spent on confirmatory replicates instead.

Inputs

• fitted Gaussian Process regression model (gpModel with mean and variance predictions)
• scaled training data (scaledX: prior gradient encodings and separation efficiency measurements)
• grid search space (gridX: all candidate unscaled gradient parameters within bounds)
• current best separation efficiency metric (scalar)
• acquisition function selector (string: 'ei', 'pi', 'ucb', 'eps', 'explore', 'exploit', or 'rand')
• epsilon parameter (float, if acqFunc='eps')
• UCB scaling factor (float, if acqFunc='ucb')

Outputs

• next gradient proposal (unscaled parameter vector to evaluate in the next LC-MS run)
• acquisition function value at selected point (scalar)
• grid indices or coordinates of the selected point

How to apply

Retrieve the trained GP model (gpModel), scaled training data (scaledX), grid search space (gridX), and the user-specified acquisition function parameter (acqFunc). Query the GP model to generate predicted mean and variance across gridX. Select the acquisition function: Expected Improvement (EI) maximizes improvement over the current best separation efficiency; Probability of Improvement (PI) maximizes the probability of any improvement; Upper Confidence Bound (UCB) balances exploration and exploitation by computing mean + (scaling factor × variance); pure exploration maximizes predicted variance; pure exploitation maximizes predicted mean; epsilon-greedy randomly samples with probability epsilon or exploits with probability (1-epsilon). Identify the grid point with the highest acquisition function value and retrieve the corresponding unscaled gradient parameters as the proposal for the next experimental run.

Related tools

• scikit-learn (Provides GaussianProcessRegressor for fitting mean and variance predictions; used to compute acquisition function values across the search space)
• BAGO (Implements the acquisition function dispatch and computeNextGradient() method that wraps acquisition function selection and returns the next gradient proposal) — https://github.com/huaxuyu/bago
• bago (Python package) (Provides programmatic support for acquisition function selection within the Bayesian optimization workflow) — https://github.com/huaxuyu/bago

Examples

from bago import computeNextGradient; next_gradient = computeNextGradient(gpModel, scaledX, gridX, current_best_efficiency, acqFunc='ei')

Evaluation signals

• The selected gradient point lies within gridX and its acquisition function value is strictly greater than or equal to all other grid points (greedy optimality).
• The returned unscaled gradient parameters are within the predefined bounds (e.g., flow rate, temperature, organic modifier range) specified at the start of optimization.
• Successive acquisition function selections produce a sequence that exhibits reduced redundancy (i.e., the same point is not proposed twice in a row unless the model has not been updated).
• Over the course of ≤10 runs, the maximum separation efficiency found increases monotonically or plateaus, indicating non-wasteful exploration.
• Comparison of acquisition functions on the same model shows that Expected Improvement and Probability of Improvement identify regions where mean+variance is high, while pure exploitation selects only the highest predicted mean, confirming functional differentiation.

Limitations

• Acquisition function effectiveness depends on the quality and diversity of prior training data; if all prior gradients cluster in a subregion of parameter space, the GP model may be poorly calibrated elsewhere and acquisition proposals may be unreliable.
• The choice of acquisition function (EI, PI, UCB, etc.) is user-specified and not automated; misalignment between the user's intention (exploration vs. exploitation) and the chosen function can waste runs.
• The method assumes the GP model accurately captures the separation efficiency landscape; if the landscape is multimodal or noisy, the model may converge to a local optimum within 10 runs.
• Epsilon-greedy and other stochastic acquisition functions introduce variability in proposals; reproducibility may require fixing random seeds.
• The grid search space (gridX) must be pre-computed and finite; for very high-dimensional gradient spaces or continuous unbounded parameters, discretization or approximation strategies are required.

Evidence

• [other] Acquisition function dispatch that proposes the next gradient: "How does BAGO select the next gradient proposal by applying an acquisition function to a fitted Gaussian Process model within the Bayesian optimization loop?"
• [methods] Expected Improvement selects points where improvement is maximized: "Expected Improvement (EI) selects points where expected improvement over current best is maximized"
• [methods] Probability of Improvement selects based on improvement probability: "Probability of Improvement (PI) selects where improvement is most probable"
• [methods] Upper Confidence Bound balances exploration and exploitation: "Upper Confidence Bound (UCB) balances exploration and exploitation"
• [methods] Pure exploration and exploitation strategies: "pure exploration maximizes predicted variance; pure exploitation maximizes predicted mean"
• [methods] Epsilon-greedy uses epsilon parameter for exploration proportion: "epsilon-greedy uses a parameter to determine the proportion of exploratory actions"
• [methods] Query GP model for mean and variance predictions: "Query the GP model to generate predicted mean and variance across the entire search space (gridX)"
• [methods] Identify highest acquisition function value: "Identify the grid point with the highest acquisition function value"
• [readme] BAGO enables acquisition function selection for efficiency: "Wonder why BAGO is efficient? Read more about acquisition functions"