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Neural architecture search applying optimal stopping theory
Matthew Sheehan1, Oleg Yakimenko1
1Department of Systems Engineering, Naval Postgraduate School, Monterey, CA, United States.
Frontiers in Artificial Intelligence
|October 9, 2025
Summary
Exploring neural architecture search (NAS) is computationally expensive. This study applies the Secretary Problem (SP) to NAS, finding that exploring approximately 37% of the search space is optimal for discovering effective neural architectures efficiently.
Area of Science:
- Artificial Intelligence
- Machine Learning
- Computer Science
Background:
- Neural Architecture Search (NAS) demands significant computational resources, limiting accessibility for many researchers.
- Early-stopping random search methods show competitive performance in NAS.
- The impracticality of exploring large NAS search spaces necessitates efficient search strategies.
Purpose of the Study:
- To determine the optimal exploration percentage of NAS search spaces for efficient architecture discovery.
- To apply optimal stopping theory, specifically the Secretary Problem (SP), to NAS.
- To investigate variants of the SP for further reducing NAS search space exploration.
Main Methods:
- Applied the Secretary Problem (SP) and its extensions ('good enough', 'call back') to NAS.
- Trained and evaluated 672 unique architectures across 20,000 runs on MNIST and CIFAR-10 datasets.
- Statistically validated findings on NAS populations ranging from 100 to 3,500 architectures.
Main Results:
- Empirically and theoretically confirmed that exploring ~37% of the NAS search space is sufficient for acceptable architecture discovery.
- The 'good enough' and 'call back' SP variants reduced exploration to ~15% and ~4%, respectively.
- Results were statistically robust across various population sizes and numerous runs.
Conclusions:
- Researchers can balance computational costs and NAS effectiveness by exploring approximately 37% of the search space using SP principles.
- SP variants offer further reductions in computational requirements for NAS.
- Provides practical guidance for implementing efficient NAS strategies.

