arXiv:2606.17319v1 Announce Type: cross Abstract: Motivated by the optimization of bounded binary black-box functions, we study the problem of learning polynomial surrogates over the Boolean hypercube. To ensure that optimizing the surrogate yields good solutions for the underlying objective, we require uniform $L_\infty$-error guarantees rather than the usual $L_2$-type guarantees. We characterize the minimax sample complexity of uniform estimation under subgaussian noise for two classes of bounded polynomials. First, for polynomials of degree at most $d$ on $n$ variables, the sample complexi
This research provides theoretical bounds for efficiently learning complex Boolean functions, a foundational problem at the core of machine learning and optimization, particularly relevant as AI systems become more sophisticated.
Improved techniques for learning and optimizing black-box functions directly impact the efficiency, robustness, and performance of AI agents and complex algorithmic systems, potentially accelerating AI development.
The research offers a pathway to more sample-efficient and uniform error guarantees for learning polynomial surrogates, which can lead to more predictable and reliable AI system behavior, especially in optimization contexts.
- · AI/ML researchers
- · Optimization software developers
- · Companies developing AI agents
- · Inefficient black-box optimization methods
- · Trial-and-error AI development paradigms
More robust and efficient training of machine learning models for complex optimization tasks.
Accelerated development and deployment of autonomous AI agents capable of navigating high-dimensional decision spaces.
New classes of AI applications become feasible due to enhanced optimization capabilities with strong theoretical guarantees.
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