Real-world optimisation problems often feature complex combinations of (1) diverse constraints, (2) discrete and mixed spaces, and are (3) highly parallelisable. (4) There are also cases where the objective function cannot be queried if unknown constraints are not satisfied, e.g. in drug discovery, safety on animal experiments (unknown constraints) must be established before human clinical trials (querying objective function) may proceed. However, most existing works target each of the above three problems in isolation and do not consider (4) unknown constraints with query rejection. For problems with diverse constraints and/or unconventional input spaces, it is difficult to apply these techniques as they are often mutually incompatible. We propose cSOBER, a domain-agnostic prudent parallel active sampler for Bayesian optimisation, based on SOBER of Adachi et al. (2023). We consider infeasibility under unknown constraints as a type of integration error that we can estimate. We propose a theoretically-driven approach that propagates such error as a tolerance in the quadrature precision that automatically balances exploitation and exploration with the expected rejection rate. Moreover, our method flexibly accommodates diverse constraints and/or discrete and mixed spaces via adaptive tolerance, including conventional zero-risk cases. We show that cSOBER outperforms competitive baselines on diverse real-world blackbox-constrained problems, including safety-constrained drug discovery, and human-relationship-aware team optimisation over graph-structured space.

翻译：现实世界中的优化问题通常具有以下复杂组合特征：（1）多样化的约束条件，（2）离散与混合空间，以及（3）高度可并行化。（4）此外，还存在目标函数在未知约束未满足时无法查询的情况，例如在药物发现中，必须先通过动物实验（未知约束）建立安全性，才能进行人体临床试验（查询目标函数）。然而，现有研究大多孤立地处理上述三个问题，未考虑（4）中伴随查询拒斥的未知约束。对于包含多样约束和/或非常规输入空间的问题，由于现有技术常相互不兼容，难以直接应用。我们提出cSOBER——一种基于Adachi等人（2023）SOBER方法的领域无关谨慎并行主动采样器，用于贝叶斯优化。我们将未知约束下的不可行性视为可估计的积分误差，并基于理论推导提出一种方法：将该误差传播为求积精度中的容差，从而自动平衡利用与探索，并考虑预期拒斥率。此外，我们的方法通过自适应容差灵活适配多样约束和/或离散与混合空间，包括传统的零风险情形。实验表明，cSOBER在多种真实世界黑箱约束问题中优于竞争基线方法，包括受安全性约束的药物发现，以及图结构空间上考虑人际关系依赖的团队优化问题。