Motivated by the imperative for real-time responsiveness and data privacy preservation, large language models (LLMs) are increasingly deployed on resource-constrained edge devices to enable localized inference. To improve output quality, retrieval-augmented generation (RAG) is an efficient technique that seamlessly integrates local data into LLMs. However, existing edge computing paradigms primarily focus on single-node optimization, neglecting opportunities to holistically exploit distributed data and heterogeneous resources through cross-node collaboration. To bridge this gap, we propose CoEdge-RAG, a hierarchical scheduling framework for retrieval-augmented LLMs in collaborative edge computing. In general, privacy constraints preclude accurate a priori acquisition of heterogeneous data distributions across edge nodes, directly impeding RAG performance optimization. Thus, we first design an online query identification mechanism using proximal policy optimization (PPO), which autonomously infers query semantics and establishes cross-domain knowledge associations in an online manner. Second, we devise a dynamic inter-node scheduling strategy that balances workloads across heterogeneous edge nodes by synergizing historical performance analytics with real-time resource thresholds. Third, we develop an intra-node scheduler based on online convex optimization, adaptively allocating query processing ratios and memory resources to optimize the latency-quality trade-off under fluctuating assigned loads. Comprehensive evaluations across diverse QA benchmarks demonstrate that our proposed method significantly boosts the performance of collaborative retrieval-augmented LLMs, achieving performance gains of 4.23\% to 91.39\% over baseline methods across all tasks.

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