The Bayesian optimization loop operates as an iterative feedback engine where a multi-armed bandit acquisition policy selects high-potential hypothesis claims to test in each round.

1. Hypothesis Generation & Selection: The seeder initializes candidate claims with prior probabilities, and an acquisition policy (such as Thompson sampling or UCB) chooses a specific claim to evaluate.
2. Snippet Ideation: An ideator model crafts a targeted rewrite or patch edit of the target content based on the selected hypothesis, while preserving grounding context.
3. Evaluation: An LLM judge module ranks the modified candidate against a competitive set across multiple samples to determine median rank outcomes.
4. Posterior Updating: Binary rewards based on whether the edit improved rank over the baseline drive Beta distribution updating (\(\alpha\) and \(\beta\) parameters), iteratively refining the system's certainty about what features maximize AI preference.