When GPU resources are limited and the hyperparameter search space is large, AWS documentation strongly recommends Bayesian optimization combined with early stopping. Bayesian optimization uses past evaluation results to intelligently select the next set of hyperparameters to test, focusing exploration on promising regions of the search space rather than testing all combinations.

In Amazon SageMaker, Bayesian optimization is the default and recommended strategy for hyperparameter tuning jobs. It significantly reduces the number of training runs required compared to grid or random search, making it highly cost-efficient for deep learning workloads.

Early stopping further improves efficiency by terminating training jobs that show poor validation performance in early epochs. This prevents wasted GPU time on configurations that are unlikely to perform well. AWS explicitly documents early stopping as a key feature for controlling training cost and duration.

Grid search and exhaustive search are computationally expensive and impractical for large hyperparameter spaces. Manual tuning is slow, error-prone, and does not scale.

By combining Bayesian optimization with early stopping, the company can rapidly converge on high-performing hyperparameter configurations while minimizing resource usage.

Therefore, Option B is the correct and AWS-aligned solution.