Amazon SageMaker Automated Model Tuning supports several hyperparameter search strategies. Bayesian optimization is explicitly designed to model the relationship between hyperparameters and objective metrics using regression techniques. Based on results from previous training jobs, Bayesian optimization predicts which hyperparameter combinations are most likely to improve model performance and evaluates those next.

AWS documentation highlights Bayesian optimization as the preferred strategy when the hyperparameter search space is small to medium and when training jobs are expensive. Because the algorithm learns from prior runs, it avoids wasting resources on unpromising configurations and converges efficiently.

Grid search exhaustively evaluates all combinations and becomes inefficient even with moderately sized search spaces. Random search does not use information from prior runs and is less efficient. Hyperband focuses on aggressive early stopping and resource allocation, not regression-based sequential selection.

Therefore, Option C is the correct and AWS-verified solution.