cs.LGMay 7, 2026

Is Escalation Worth It? A Decision-Theoretic Characterization of LLM Cascades

Authors: Dylan Bouchard

Abstract

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 kk models, we characterize the frontier achievable by deterministic two-model threshold cascades as the pointwise envelope over (k2)\binom{k}{2} pairwise cascades, with switching points where the optimal pair changes. For kk-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.

Explore similar work

CardsList
Jun 25, 2026cs.PF

Cluster, Route, Escalate: Cascaded Framework for Cost-Aware LLM Serving

Efficient deployment of large language models (LLMs) in production forces a trade-off between accuracy and cost. Operators often default to a single model that is either expensive for easy queries or insufficient for hard ones. To address this challenge, we propose a two-stage cascaded solution. Stage 1 clusters incoming queries and assigns each cluster to its most cost-effective model. The cost budget for this routing process is set by an interpretable hyperparameter, tuned offline. Stage 2 adds a quality estimation (QE) cascade; when an output from Stage 1 is judged low-quality, the query is escalated to a stronger model. This ensures only hard or low-confidence cases reach the expensive models. On the test datasets, the cascaded system retains 97-99% of the strongest model's accuracy while reducing Time Per Output Token (TPOT). It requires only task-correctness labels and adapts to changes in the model pool without manual reconfiguration.
Yasmin Moslem, Magdalena Kacmajor, Vasudevan Nedumpozhimana +11
Large Language Model ServingEscalationHyperparameter Optimization
AskPDF
Jul 27, 2026cs.LG

Conformal Cascade: Distribution-Free Accuracy Guarantees for Multi-Tier LLM Inference

Large language model (LLM) cascades reduce inference cost by routing easy queries to a small model and deferring hard queries to a larger one. Production cascades govern this deferral through a confidence threshold, but LLM confidence scores are miscalibrated, the threshold must be tuned per model pair and per domain, and no setting yields a formal bound on cascade accuracy. We introduce \textbf{Conformal Cascade} (CC), a multi-tier inference framework that uses conformal prediction set size as the deferral rule: accept when the calibrated set collapses to a single answer, defer otherwise. The procedure delivers a distribution-free, finite-sample accuracy guarantee. By a per-tier union bound, the prediction set at the accepting tier covers the correct answer with probability at least 1−Kα1 - Kα for any user-specified αα; under a selection-preservation condition (consistent with, but not strictly implied by, our marginal coverage results), the bound tightens to 1−α1 - α. We further characterise expected cascade cost as an explicit function of αα and the calibration-set acceptance rate. Across 18 multiple-choice benchmarks spanning science, medicine, commonsense, and standardized exams, evaluated on two-tier cascades drawn from four open-weight model families, CC strictly improves over the strongest calibration-tuned heuristic cascade on the majority of family--benchmark pairs, with the largest gains on reasoning-heavy benchmarks where majority vote is unreliable; on easier benchmarks the cascade commits the vast majority of queries to the small model at no accuracy cost. Extension to open-ended generation requires an answer-clustering step that we leave for future work. The method requires no model training and only black-box API access.
Yifan Dou, Shikan Lian, Shibo Li
LLM Inference EfficiencyConformal Calibration
AskPDF
May 11, 2026cs.LG

UCCI: Calibrated Uncertainty for Cost-Optimal LLM Cascade Routing

LLM cascades and model routing promise lower inference cost by sending easy queries to a small model and escalating hard ones to a large model, but most deployed routers use uncalibrated confidence scores and require per-workload threshold tuning. We present UCCI, a calibration-first router that maps token-level margin uncertainty to a per-query error probability via isotonic regression and selects the escalation threshold by constrained cost minimization. Under three explicit assumptions, threshold policies on the calibrated score are cost-optimal, and isotonic calibration achieves O(n^{-1/3}) sample complexity for expected calibration error (ECE). On a production named entity recognition workload of 75,000 queries served by 4B and 12B instruction-tuned LLMs on H100 GPUs, UCCI cuts inference cost by 31% (95% CI: [27%, 35%]) at micro-F1 = 0.91 while reducing ECE from 0.12 to 0.03. At the same operating point, UCCI beats entropy thresholding, split-conformal routing, and a FrugalGPT-style learned threshold. All cascade results use end-to-end routing on actual model outputs and measured H100 latency, not simulated routing from global accuracies or nominal API prices.
Varun Kotte
Large Language Model RoutingInference CostCalibrated Uncertainty
AskPDF