Bayesian optimization (BO) is a powerful approach to sample-efficient optimization of black-box objective functions. However, the application of BO to areas such as recommendation systems often requires taking the interpretability and simplicity of the configurations into consideration, a setting that has not been previously studied in the BO literature. To make BO useful for this setting, we present several regularization-based approaches that allow us to discover sparse and more interpretable configurations. We propose a novel differentiable relaxation based on homotopy continuation that makes it possible to target sparsity by working directly with $L_0$ regularization. We identify failure modes for regularized BO and develop a hyperparameter-free method, sparsity exploring Bayesian optimization (SEBO) that seeks to simultaneously maximize a target objective and sparsity. SEBO and methods based on fixed regularization are evaluated on synthetic and real-world problems, and we show that we are able to efficiently optimize for sparsity.

翻译：贝叶斯优化（BO）是一种高效的样本优化方法，适用于黑箱目标函数的优化。然而，将BO应用于推荐系统等领域时，通常需要考虑配置的可解释性和简洁性，而这一设定在BO文献中尚未被研究。为使BO在此设定中发挥作用，我们提出了若干基于正则化的方法，以发现稀疏且更具解释性的配置。我们提出了一种基于同伦延拓的新型可微松弛方法，通过直接采用$L_0$正则化来针对稀疏性进行优化。我们识别了正则化BO的失效模式，并开发了一种无超参数的方法——稀疏探索贝叶斯优化（SEBO），该方法旨在同时最大化目标函数和稀疏性。SEBO及基于固定正则化的方法在合成问题与实际问题中进行了评估，结果表明我们能够高效地优化稀疏性。