Set-Valued Routing for Language-Model Agent Systems: A WildChat Benchmark and Cost-Aware Evaluation

Abstract

Language-model agent systems must map natural-language requests to one or more specialized agents before planning or tool execution. This decision is often treated as top-1 selection, although compositional requests can require several capabilities and unnecessary dispatch raises cost. We formulate fixed-catalog routing as set-valued language understanding and construct a benchmark of 3,000 WildChat prompts over 12 capability-defined agents. Reproducible schema-guided reference sets are balanced by agent frequency and route cardinality. We compare profile retrieval, multilabel classifiers, a fine-tuned text encoder, and catalog-conditioned zero-shot GPT-4o. Evaluation combines set quality, latency, capability coverage, and ordinal-cost utility. The encoder attains 89.59 F1, compared with 71.79 for linear SVM and 41.51 for GPT-4o, and retains 88.02 F1 under a harder semantic-group split. We further introduce Weighted Agent Routing (WAR), a deterministic post-scoring rule that changes the quality-cost operating point without retraining; Encoder+WAR obtains the best constrained utility. The results show that catalog-specific supervision and explicit set construction are important for multi-agent dispatch, while cost-aware decision layers can complement strong language encoders.