From Sorting Algorithms to Scalable Kernels: Bayesian Optimization in High-Dimensional Permutation Spaces
arXiv:2507.13263v4 Announce Type: replace-cross Abstract: Bayesian Optimization (BO) is a powerful tool for black-box optimization, but its application to high-dimensional permutation spaces is severely limited by the challenge of defining scalable representations. The current state-of-the-art BO approach for permutation spaces relies on an exhaustive $\Omega(n^2)$ pairwise comparison, inducing a dense representation that is impractical for large-scale permutations. To break this barrier, we introduce a novel framework for generating efficient permutation representations via kernel functions d
The continuous drive to scale AI applications necessitates more efficient and robust optimization methods, particularly in complex, high-dimensional spaces that current techniques struggle with.
This research addresses a fundamental limitation in applying Bayesian Optimization to large-scale permutation problems, which are crucial for advancing various AI domains from deep learning architecture search to resource allocation.
The proposed 'scalable kernel' framework offers a path to apply powerful black-box optimization techniques to problems previously considered intractable due to the computational cost of representing high-dimensional permutation spaces.
- · AI researchers and developers
- · Companies using AI for optimization
- · Developers of AutoML platforms
Black-box optimization problems involving permutations become more tractable and efficient to solve.
Improved efficiency in areas like neural architecture search, scheduling, and resource allocation within complex systems.
Accelerated development of AI systems that rely on optimizing discrete and combinatorial structures, potentially leading to new breakthroughs.
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Read at arXiv cs.AI