Optimizing the communication structure of large language model based multi-agent systems (LLM-MAS) has been shown to improve downstream performance and reduce token usage. Existing methods typically rely on randomly sampled training tasks. However, tasks may differ substantially in difficulty and domain, and thus they are not equally informative for updating communication structure, making optimization often unstable and highly sensitive to the particular training set. To actively identify the most valuable tasks for communication-structure optimization, we propose an ensemble-based information-theoretic task selection framework. The proposed method estimates task informativeness by how much a candidate task changes the distribution over graph parameters, using ensemble Kalman inversion as an efficient and derivative-free approximation of the corresponding Bayesian update. The resulting estimator is especially suitable for black-box and noisy multi-agent systems. To enhance scalability, we construct a compact candidate pool through embedding-based representative selection and combine the informative selection with surrogate modeling and batch Thompson sampling. We validate the proposed framework across both benign and adversarial settings and multiple task formats. It consistently outperforms random training, demonstrating more effective task selection and greater overall cost efficiency.

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