Automatic performance tuning (auto-tuning) is essential for optimizing high-performance applications, where vast and irregular parameter spaces make manual exploration infeasible. Traditionally, auto-tuning relies on well-established optimization algorithms such as evolutionary algorithms, annealing methods, or surrogate model-based optimizers to efficiently find near-optimal configurations. However, designing effective optimizers remains challenging, as no single method performs best across all tuning tasks. In this work, we explore a new paradigm: using large language models (LLMs) to automatically generate optimization algorithms tailored to auto-tuning problems. We introduce a framework that prompts LLMs with problem descriptions and search-space characteristics results to produce specialized optimization strategies, which are iteratively examined and improved. These generated algorithms are evaluated on four real-world auto-tuning applications across six hardware platforms and compared against the state-of-the-art in optimization algorithms of two contemporary auto-tuning frameworks. The evaluation demonstrates that providing additional application- and search space-specific information in the generation stage results in an average performance improvement of 30.7\% and 14.6\%, respectively. In addition, our results show that LLM-generated optimizers can rival, and in various cases outperform, existing human-designed algorithms, with our best-performing generated optimization algorithms achieving, on average, 72.4\% improvement over state-of-the-art optimizers for auto-tuning.

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