This paper proposes novel noise-free Bayesian optimization strategies that rely on a random exploration step to enhance the accuracy of Gaussian process surrogate models. The new algorithms retain the ease of implementation of the classical GP-UCB algorithm, but the additional random exploration step accelerates their convergence, nearly achieving the optimal convergence rate. Furthermore, to facilitate Bayesian inference with an intractable likelihood, we propose to utilize optimization iterates for maximum a posteriori estimation to build a Gaussian process surrogate model for the unnormalized log-posterior density. We provide bounds for the Hellinger distance between the true and the approximate posterior distributions in terms of the number of design points. We demonstrate the effectiveness of our Bayesian optimization algorithms in non-convex benchmark objective functions, in a machine learning hyperparameter tuning problem, and in a black-box engineering design problem. The effectiveness of our posterior approximation approach is demonstrated in two Bayesian inference problems for parameters of dynamical systems.

翻译：本文提出了新颖的无噪声贝叶斯优化策略，该策略通过随机探索步骤来提升高斯过程代理模型的准确性。新算法保留了经典GP-UCB算法易于实现的特性，但额外的随机探索步骤加速了其收敛速度，几乎达到了最优收敛率。此外，为促进具有难处理似然函数的贝叶斯推断，我们提出利用优化迭代进行最大后验估计，从而为未归一化的对数后验密度构建高斯过程代理模型。我们基于设计点数量给出了真实后验分布与近似后验分布之间海林格距离的界。我们在非凸基准目标函数、机器学习超参数调优问题以及黑盒工程设计问题中验证了所提贝叶斯优化算法的有效性。在两个动态系统参数的贝叶斯推断问题中，我们证明了所提后验近似方法的有效性。