BayesianAgent: Guiding Agentic Evolution with Bayesian Optimization

Agents that iteratively improve executable solutions must allocate a limited experimental budget across a growing set of candidates. Most existing systems use rule-based selection informed by observed performance and experimental history. However, these rules do not explicitly learn to predict the gain from the next expansion and quantify uncertainty in that prediction. We introduce **BayesianAgent**, a Bayesian optimization approach that learns where to invest further experiments from completed outcomes. Its central intuition is that an experiment can inform the improvement potential of related candidates, including those with little direct evidence. A Gaussian process learns expansion gains and their uncertainty, sharing evidence across candidates. Joint Thompson sampling then selects the next candidate to expand, balancing promising refinements with opportunities whose value remains uncertain. We compare all methods using Muse Spark 1.3 under matched experimental budgets. Across 15 AlphaEvolve mathematical optimization tasks and 22 MLE-bench Lite tasks, BayesianAgent outperforms the MLEvolve baseline. It achieves the best AlphaEvolve average rank (1.83), the highest MLE-bench Lite gold rate (**45.45%**), and a joint-highest medal rate (**72.73%**) among evaluated methods. Further analysis shows that its predictions rank observed expansion gains more accurately than MLEvolve's historical rewards. These results support learning from experimental outcomes to guide subsequent allocation in agentic evolution. Our code is available at https://anonymous.4open.science/r/BayesianAgent-anonymous-6EBB.