Constrained Bayesian Optimization with Improvement Policy

In Bayesian optimization, Expected Improvement (EI) is widely used for unconstrained optimization but lacks effective handling of constraints. Existing approaches modify EI by incorporating feasibility probabilities, requiring an initial feasible point, and often restricting exploration to the feasible region. This article introduces a novel improvement-based acquisition function designed to address these limitations. The proposed function strikes a balance between exploration and exploitation across both feasible and infeasible regions. We evaluate our framework against state-of-the-art methods on four benchmark problems and apply it to groundwater remediation in hydrology and hyperparameter tuning of neural networks.