Is Escalation Worth It? A Decision-Theoretic Characterization of LLM Cascades
For practitioners deploying LLM cascades, the paper provides theoretical insights and empirical evidence that cascade performance is limited by structural cost rather than intermediate stages, guiding more efficient cost-quality tradeoffs.
The paper develops a decision-theoretic framework for LLM cascades, characterizing the cost-quality frontier and showing that pairwise cascades often match or outperform more complex k-model cascades. On five benchmarks, a pre-generation router outperforms cascades on four datasets, primarily by avoiding the cheap model's generation cost on queries sent directly to a larger model.
Model cascades, in which a cheap LLM defers to an expensive one on low-confidence queries, are widely used to navigate the cost-quality tradeoff at deployment. Existing approaches largely treat the deferral threshold as an empirical hyperparameter, with limited guidance on the geometry of the resulting cost-quality frontier over a model pool. We develop a decision-theoretic framework grounded in constrained optimization and duality. For a two-model cascade, we establish piecewise concavity of the cost-quality frontier on decreasing-benefit regions of the confidence support, with reciprocal shadow prices linking the budget- and quality-constrained formulations. Given a pool of $k$ models, we characterize the frontier achievable by deterministic two-model threshold cascades as the pointwise envelope over $\binom{k}{2}$ pairwise cascades, with switching points where the optimal pair changes. For $k$-model cascades, we derive first-order conditions in which a single shadow price equalizes marginal quality-per-cost across stage boundaries. We validate the framework on five benchmarks (MATH, MMLU, TriviaQA, SimpleQA, LiveCodeBench) across eight models from five providers. Within the deterministic threshold-cascade class, full fixed chains underperform the pairwise envelope, and optimized subsequence cascades do not deliver practically meaningful held-out gains over it. A lightweight pre-generation router exceeds the best cascade policy on four of five datasets, mainly because it avoids the cheap model's generation cost on queries sent directly to a larger model rather than because of a stronger routing signal. These results suggest that cascade performance is limited primarily by structural cost, since cascades pay the cheap model before any escalation decision, rather than by a shortage of intermediate stages.