BayeSQP：通过序列二次规划进行贝叶斯优化
BayeSQP: Bayesian Optimization through Sequential Quadratic Programming
AI总结：
BayeSQP通过结合序列二次规划与贝叶斯优化，提供了一个灵活的框架，用于高维黑箱优化问题，优于现有方法。
摘要：
我们介绍了一个新的算法BayeSQP，用于一般的黑箱优化问题，该算法将序列二次规划的结构与贝叶斯优化的概念相结合。BayeSQP使用二次高斯过程代理来建模目标函数和约束函数的值、梯度和Hessian，仅利用零阶信息。在每次迭代中，利用GP后验估计构建一个局部子问题并求解以获得搜索方向。关键在于子问题的构建明确地纳入了函数和导数估计的不确定性，从而得到一个可解的二次锥规划，以实现高概率的改进。随后通过受约束的汤普森采样进行一维线搜索以选择下一个评估点。实验结果表明，BayeSQP在特定的高维设置中优于最先进的方法。我们的算法提供了一个原理上合理且灵活的框架，将经典的优化技术与现代的黑箱优化方法相结合。
英文摘要：
We introduce BayeSQP, a novel algorithm for general black-box optimization that merges the structure of sequential quadratic programming with concepts from Bayesian optimization. BayeSQP employs second-order Gaussian process surrogates for both the objective and constraints to jointly model the function values, gradients, and Hessian from only zero-order information. At each iteration, a local subproblem is constructed using the GP posterior estimates and solved to obtain a search direction. Crucially, the formulation of the subproblem explicitly incorporates uncertainty in both the function and derivative estimates, resulting in a tractable second-order cone program for high probability improvements under model uncertainty. A subsequent one-dimensional line search via constrained Thompson sampling selects the next evaluation point. Empirical results show thatBayeSQP outperforms state-of-the-art methods in specific high-dimensional settings. Our algorithm offers a principled and flexible framework that bridges classical optimization techniques with modern approaches to black-box optimization.
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