Which Model for Which Role? Cost-Efficient Pareto Recommendation for LLM Agentic Workflows

LLM agentic workflows increasingly employ different models for specialized roles. Choosing among these assignments requires balancing task quality against per-query API cost. Finding good assignments incurs a separate search cost from evaluating multiple candidates. We introduce Cost-Coupled Gittins (CC-Gittins), which exploits a shared cost structure: assignments that cost more to run also cost more to evaluate. Gittins controllers for quality and cost share observations and independently relax their evaluation-cost penalties to allocate further evaluations. We evaluate CC-Gittins by offline replay on eight quality-cost matrices from workflows with two to five roles and up to 1,681 candidate assignments. Across the eight quality-cost benchmarks, CC-Gittins recovers a substantial fraction of the true Pareto frontier with few false positives at roughly 10% of the exhaustive-evaluation cost, and recovers most of the frontier by 30%.