BiCSRouter: Bi-Level Cross-System Routing for Utility-Aware LLM Inference

Selecting an appropriate LLM configuration for a given query is critical, yet existing routing frameworks operate within a single computational paradigm. To address this gap, we formalize the Cross-System Routing Problem, a hierarchical decision-making task that decomposes routing into intra-regime configuration selection and inter-regime system selection. Building on this, we propose BiCSRouter, a bilevel cross-system routing framework that integrates two orthogonal regimes: intensive reasoning via single-agent systems and extensive collaboration via multi-agent systems. BiC-SRouter performs policy learning within each system and employs a lightweight inter-regime router that selects the optimal regime based on predicted performance and cost. Experiments on the MBPP and MATH benchmarks demonstrate that BiCSRouter outperforms 15 representative baselines across three types. On MBPP, compared to the performance ceiling of GPT-5, BiCSRouter achieves a 46% reduction in cost with only a 2% drop in accuracy. Finally, we show that BiCSRouter can extend to additional regimes, highlighting its generality as a cross-system routing framework.