c-TPE: Tree-structured Parzen Estimator with Inequality Constraints for Expensive Hyperparameter Optimization

Hyperparameter optimization (HPO) is crucial for strong performance of deep learning algorithms and real-world applications often impose some constraints, such as on memory usage or latency, on top of the performance requirement. In this work, we propose constrained TPE (c-TPE), an extension of the widely-used versatile Bayesian optimization method, tree-structured Parzen estimator (TPE), to handle these constraints. Our proposed extension goes beyond a simple combination of an existing acquisition function and the original TPE, and instead includes modifications that address issues that cause poor performance. We thoroughly analyze these modifications both empirically and theoretically, providing insights into how they effectively overcome these challenges. In the experiments, we demonstrate that c-TPE exhibits the best average rank performance among existing methods with statistical significance on 81 expensive HPO problems with inequality constraints. Due to the lack of baselines, we only discuss the applicability of our method to hard-constrained optimization in Appendix D. The implementation is now available via OptunaHub.