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As scaling large language models faces prohibitive costs, multi-agent systems emerge as a promising alternative, though challenged by static knowledge assumptions and coordination inefficiencies. We introduce Knowledge-Aware Bayesian Bandits (KABB), a novel framework that enhances multi-agent system coordination through semantic understanding and dynamic adaptation. The framework features three key innovations: a customized knowledge distance model for deep semantic understanding, a dual-adaptation mechanism for continuous expert optimization, and a knowledge-aware Thompson Sampling strategy for efficient expert selection. Extensive evaluation demonstrates KABB achieves an optimal cost-performance balance, maintaining high performance while keeping computational demands relatively low in multi-agent coordination.