Local Constrained Bayesian Optimization

Trust Region Bayesian Optimization (TuRBO) is an effective strategy for alleviating the curse of dimensionality in high-dimensional black-box optimization. However, inappropriate lengthscale design can cause the local Gaussian process (GP) model within the trust region to degenerate, leading to suboptimal performance in high dimensions. In this work, we show that TuRBO's local GP may remain either excessively complex or overly simple as the dimension $D$ and trust region side length $L$ vary. To address this issue, we propose a straightforward variant, AdaScale-TuRBO, which scales the GP lengthscale with both the problem dimension and trust region size, thereby preserving kernel geometry and maintaining consistent prior complexity. Empirically, we show that AdaScale-TuRBO can robustly outperform standard TuRBO and other popular high-dimensional BO methods on synthetic benchmarks and real-world trajectory planning tasks.

Expensive constrained optimization problems in real-world industry design often involve constraint thresholds that are difficult to determine in advance. Engineers may need to adjust constraint thresholds to explore different feasibility-performance trade-offs, requiring solutions under a wide range of threshold settings. However, existing constrained Bayesian optimization methods treat each threshold configuration independently, leading to repeated optimization and failing to exploit the shared relationship among continuously varying thresholds. To address this challenge, we propose constraint-bound agnostic Bayesian optimization (CBA-BO), a learning-based framework that learns a parametric constraint model mapping thresholds to optimal solutions. Once learned, CBA-BO directly predicts solutions for arbitrary unseen threshold configurations without additional optimization, with a one-step Bayesian optimization refinement further improving solution quality. Experiments on benchmark and engineering problems demonstrate that CBA-BO learns a transferable threshold-solution mapping, enabling efficient prediction and optimization for arbitrary threshold queries. An intent-guided constraint-bound recommendation mechanism is further developed to improve objective performance while satisfying user-specified constraint preferences.

Bayesian Optimisation (BO) under unknown constraints is particularly challenging when feasible regions are small. In such settings, existing methods that typically rely solely on evaluations of the true objective and constraints struggle to efficiently explore the design space. However, many real-world applications offer auxiliary data sources (e.g. surrogate models or simplified simulations) that can support early exploration. Despite this potential, their integration into constrained BO remains largely unexplored. We propose a general multi-source framework that extends constrained Max-value Entropy Search, capturing inter-source correlation while balancing evaluation cost and information gain. Experiments on both synthetic and physics-based benchmarks show that our method efficiently identifies feasible and optimal solutions, even when auxiliary data are only weakly correlated. The proposed approach consistently outperforms existing methods, particularly in early-stage exploration.