C3PO: Optimized Large Language Model Cascades with Probabilistic Cost Constraints for Reasoning
Antonios Valkanas, Soumyasundar Pal, Pavel Rumiantsev, Yingxue Zhang, Mark Coates
Large language models (LLMs) have achieved impressive results on complex reasoning tasks, but their high inference cost remains a major barrier to real-world deployment. A promising solution is to use cascaded inference, where small, cheap models handle easy queries, and only the hardest examples are escalated to more powerful models. However, existing cascade methods typically rely on supervised training with labeled data, offer no theoretical generalization guarantees, and provide limited control over test-time computational cost. We introduce **C3PO** (*Cost Controlled Cascaded Prediction Optimization*), a self-supervised framework for optimizing LLM cascades under probabilistic cost constraints. By focusing on minimizing regret with respect to the most powerful model, C3PO avoids the need for labeled data by constructing a cascade using only unlabeled model outputs. It leverages conformal prediction to bound the probability that inference cost exceeds a user-specified budget. We provide theoretical guarantees on both cost control and generalization error, and show that our optimization procedure is effective even with small calibration sets. Empirically, C3PO achieves *state-of-the-art* performance across a diverse set of reasoning benchmarks—including GSM8K, MATH500, and BigBench-Hard—outperforming strong LLM cascading baselines in both accuracy and cost-efficiency. Our results demonstrate that principled, label-free cascade optimization can enable scalable and reliable LLM deployment.