Organizations: Shenzhen International Center for Industrial and Applied Mathematics · Shenzhen Research Institute of Big Data · The Chinese University of Hong Kong, Shenzhen · Shenzhen Campus of Sun Yat-sen University · Shenzhen Loop Area Institute
Abstract
Routing each query to a cost-effective large language model (LLM) is critical for balancing quality and cost, yet most routers rely on a centralized task center to predict model performance, creating an information-risk mismatch and a scalability bottleneck as the model pool grows. We propose a market-based routing paradigm that shifts ex-ante prediction to LLM providers via a reverse auction, where providers bid with self-predicted success probabilities and execution costs. To account for inherently noisy provider predictions and center evaluations, we introduce the \textit{\textbf{E}rror-\textbf{A}ware \textbf{R}everse \textbf{A}uction \textbf{M}echanism} (EA-RAM), which explicitly models this inherent Dual Error. We prove that EA-RAM is Bayesian incentive compatible and individually rational under the Dual Error, establish sufficient conditions for center rationality, and derive an explicit welfare-loss bound. We further identify robustness effects: opposite-signed errors can cancel, vanishing-tail link functions (e.g., logistic) stabilize clear-cut cases via saturation, and extra noise smooths belief maps, reducing the gains from marginal manipulation. Experiments on simulations and real-world benchmarks show that EA-RAM is robust to the Dual Error and achieves a better cost--performance Pareto frontier than centralized baselines, with additional gains when providers contribute local information, validating its practical effectiveness.
Large language models (LLMs) achieve impressive performance across multiple domains, but using the most capable model for every query is prohibitive at scale. LLM routing exploits diversity in model capability and cost by assigning each query to a suitable model to balance utility and budget. Current methods have two limitations: (i) they either use heuristics that do not always enforce the budget constraint or impose a fixed per-query budget that cannot adapt across the workload and leads to suboptimal performance; (ii) they require supervised learning on a dense dataset with statistics for every query-model pair, which is expensive to collect. To address these challenges, we formulate LLM routing as a constrained contextual multi-armed bandit problem and introduce WISERouter (WR for short), a framework that supports offline learning from historical interactions as well as online learning with exploration. We further prove that WR-Online achieves a sublinear regret bound of O(T) over a time horizon T. Empirical results on RouterBench and SWE-Bench demonstrate that (i) WR-Offline surpasses existing baselines in performance under a fixed budget and adheres more closely to budget constraints, and (ii) WR-Online achieves comparable performance to the baselines, while using substantially less exploration data.
Inference costs for large language model (LLM) applications are rapidly growing, driven by surging demand and rising infrastructure cost. Users expect high-quality responses, and in commercial settings this is formally codified in Service Level Agreements (SLAs), creating a fundamental tension between cost and quality. Recent progress on cost-aware LLM request routing has shown potential to resolve this tension, but existing approaches rely on complete feedback signals, offline training, extensive per-workload tuning, and most lack SLA guarantees or inference-time adaptivity. We introduce SLARouter, an online routing algorithm that learns a cost-optimal policy from the sparse, one-sided user feedback available in production systems. SLARouter provides theoretical guarantees for both cost optimality and strict SLA compliance. Experiments across a wide range of LLM benchmarks show that SLARouter satisfies SLA constraints without the need for per-benchmark tuning, reducing operating cost by up to 2.2x over existing baselines.
Herbert Woisetschläger, Arastun Mammadli, Ryan Zhang +1
No single large language model (LLM) is optimal across all queries and budget constraints, making model routing essential for cost-effective deployment. Existing routers adopt diverse formulations and implementations, making fair comparison and extension difficult. We present a unified formulation of LLM routing as a sequential decision process characterized by five components: context encoders, model encoders, scoring functions, decision rules, and learning signals, covering single-turn, multi-turn, and personalized routing. Based on this formulation, we develop an automated pipeline for constructing routing supervision and evaluating routers jointly on response quality and inference cost. The resulting benchmark, xRouteBench, spans generic LLM, memory-augmented, vision, time-series, and personalized routing tasks. We further introduce LLMRouter, an open-source modular infrastructure with more than 16 representative routers. Our empirical study shows that learned routers outperform the strongest fixed-model baseline by 14.6% relatively, lightweight routers become more competitive under tight cost constraints, and user-conditioned routing consistently improves personalization.