Bayesian optimization (BO) is widely used for black-box optimization
problems, and have been shown to perform well in various real-world tasks.
However, most of the existing BO methods aim to learn the optimal solution,
which may become infeasible when the parameter space is extremely large or the
problem is time-sensitive. In these contexts, switching to a satisficing
solution that requires less information can result in better performance. In
this work, we focus on time-sensitive black-box optimization problems and
propose satisficing Thompson sampling-based parallel Bayesian optimization
(STS-PBO) approaches, including synchronous and asynchronous versions. We shift
the target from an optimal solution to a satisficing solution that is easier to
learn. The rate-distortion theory is introduced to construct a loss function
that balances the amount of information that needs to be learned with
sub-optimality, and the Blahut-Arimoto algorithm is adopted to compute the
target solution that reaches the minimum information rate under the distortion
limit at each step. Both discounted and undiscounted Bayesian cumulative regret
bounds are theoretically derived for the proposed STS-PBO approaches. The
effectiveness of the proposed methods is demonstrated on a fast-charging design
problem of Lithium-ion batteries. The results are accordant with theoretical
analyses, and show that our STS-PBO methods outperform both sequential
counterparts and parallel BO with traditional Thompson sampling in both
synchronous and asynchronous settings.

本研究针对时间敏感的黑盒优化问题，提出了满足条件的基于 Thompson 抽样的并行贝叶斯优化（STS-PBO）方法，引入了速率失真理论构建平衡学习所需信息量和次优性的损失函数，并采用 Blahut-Arimoto 算法在每一步计算达到最小信息速率的目标解，实验证明我们的 STS-PBO 方法在同步和异步设置中均优于串行方法和传统 Thompson 抽样的并行贝叶斯优化方法。