Black-box optimization is essential for tuning complex machine learning algorithms which are easier to experiment with than to understand. In this paper, we show that a simple ensemble of black-box optimization algorithms can outperform any single one of them. However, searching for such an optimal ensemble requires a large number of experiments. We propose a Multi-GPU-optimized framework to accelerate a brute force search for the optimal ensemble of black-box optimization algorithms by running many experiments in parallel. The lightweight optimizations are performed by CPU while expensive model training and evaluations are assigned to GPUs. The multi-GPU solution achieves 10x speedup of the CPU implementation.

Aggregating multiple learners through an ensemble of models aims to make better predictions by capturing the underlying distribution more accurately. Different ensembling methods, such as bagging, boosting and stacking/blending, have been studied and adopted extensively in research and practice. While bagging and boosting intend to reduce variance and bias, respectively, blending approaches target both by finding the optimal way to combine base learners to find the best trade-off between bias and variance. In blending, ensembles are created from weighted averages of multiple base learners. In this study, a systematic approach is proposed to find the optimal weights to create these ensembles for bias-variance tradeoff using cross-validation for regression problems (Cross-validated Optimal Weighted Ensemble (COWE)). Furthermore, it is known that tuning hyperparameters of each base learner inside the ensemble weight optimization process can produce better performing ensembles. To this end, a nested algorithm based on bi-level optimization that considers tuning hyperparameters as well as finding the optimal weights to combine ensembles (Cross-validated Optimal Weighted Ensemble with Internally Tuned Hyperparameters (COWE-ITH)) was proposed. The algorithm is shown to be generalizable to real data sets though analyses with ten publicly available data sets. The prediction accuracies of COWE-ITH and COWE have been compared to base learners and the state-of-art ensemble methods. The results show that COWE-ITH outperforms other benchmarks as well as base learners in 9 out of 10 data sets.