Automatic performance tuning (auto-tuning) is widely used to optimize performance-critical applications across many scientific domains by finding the best program variant among many choices. Efficient optimization algorithms are crucial for navigating the vast and complex search spaces in auto-tuning. As is well known in the context of machine learning and similar fields, hyperparameters critically shape optimization algorithm efficiency. Yet for auto-tuning frameworks, these hyperparameters are almost never tuned, and their potential performance impact has not been studied. We present a novel method for general hyperparameter tuning of optimization algorithms for auto-tuning, thus "tuning the tuner". In particular, we propose a robust statistical method for evaluating hyperparameter performance across search spaces, publish a FAIR data set and software for reproducibility, and present a simulation mode that replays previously recorded tuning data, lowering the costs of hyperparameter tuning by two orders of magnitude. We show that even limited hyperparameter tuning can improve auto-tuner performance by 94.8% on average, and establish that the hyperparameters themselves can be optimized efficiently with meta-strategies (with an average improvement of 204.7%), demonstrating the often overlooked hyperparameter tuning as a powerful technique for advancing auto-tuning research and practice.

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