We present mlr3mbo, a comprehensive and modular toolbox for Bayesian optimization in R. mlr3mbo supports single- and multi-objective optimization, multi-point proposals, batch and asynchronous parallelization, input and output transformations, and robust error handling. While it can be used for many standard Bayesian optimization variants in applied settings, researchers can also construct custom BO algorithms from its flexible building blocks. In addition to an introduction to the software, its design principles, and its building blocks, the paper presents two extensive empirical evaluations of the software on the surrogate-based benchmark suite YAHPO Gym. To identify robust default configurations for both numeric and mixed-hierarchical optimization regimes, and to gain further insights into the respective impacts of individual settings, we run a coordinate descent search over the mlr3mbo configuration space and analyze its results. Furthermore, we demonstrate that mlr3mbo achieves state-of-the-art performance by benchmarking it against a wide range of optimizers, including HEBO, SMAC3, Ax, and Optuna.

In contrast, in non-private settings, practitioners commonly utilize "adaptive" hyperparameter optimization methods such as Gaussian process-based optimization, which select the next candidate based on information gathered from previous outputs. This substantial contrast between private and non-private hyperparameter optimization underscores a critical concern. In our paper, we introduce DP-HyPO, a pioneering framework for "adaptive"

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An automatic approach to adapting these hyperparameters would improve performance and simplifytheengineering process.

Toaddress theabovechallenges, wepropose anovelhyperparameter mutation (HPM) scheduling algorithm in this study, which adopts a population based training framework to explicitly learn a trade-off (i.e., a mutation schedule) between using the hypergradient-guided local search and the mutation-driven global search.