# WISERouter: LLM Routing with Workload Budget Constraint

arXiv: https://arxiv.org/abs/2607.23765 · HTML: https://mlsanity.com/paper/2607.23765/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 42 references that are in the map.
- First posted on arXiv 26 Jul 2026.

## Builds on (most cited first, 28 of 28)

- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [SWE-bench: Can Language Models Resolve Real-World GitHub Issues?](https://mlsanity.com/paper/2310.06770/) (2023)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [Chatbot Arena: An Open Platform for Evaluating LLMs by Human Preference](https://mlsanity.com/paper/2403.04132/) (2024)
- [Accelerating Large Language Model Decoding with Speculative Sampling](https://mlsanity.com/paper/2302.01318/) (2023)
- [FrugalGPT: How to Use Large Language Models While Reducing Cost and Improving Performance](https://mlsanity.com/paper/2305.05176/) (2023)
- [RouteLLM: Learning to Route LLMs with Preference Data](https://mlsanity.com/paper/2406.18665/) (2024)
- [LLM-Blender: Ensembling Large Language Models with Pairwise Ranking and Generative Fusion](https://mlsanity.com/paper/2306.02561/) (2023)
- [PyramidKV: Dynamic KV Cache Compression based on Pyramidal Information Funneling](https://mlsanity.com/paper/2406.02069/) (2024)
- [Hybrid LLM: Cost-Efficient and Quality-Aware Query Routing](https://mlsanity.com/paper/2404.14618/) (2024)
- [RouterBench: A Benchmark for Multi-LLM Routing System](https://mlsanity.com/paper/2403.12031/) (2024)
- [Routing to the Expert: Efficient Reward-guided Ensemble of Large Language Models](https://mlsanity.com/paper/2311.08692/) (2023)
- [Large Language Model Cascades with Mixture of Thoughts Representations for Cost-efficient Reasoning](https://mlsanity.com/paper/2310.03094/) (2023)
- [Language Model Cascades: Token-level uncertainty and beyond](https://mlsanity.com/paper/2404.10136/) (2024)
- [S3: Increasing GPU Utilization during Generative Inference for Higher Throughput](https://mlsanity.com/paper/2306.06000/) (2023)
- [A Unified Approach to Routing and Cascading for LLMs](https://mlsanity.com/paper/2410.10347/) (2024)
- [Ensemble Learning for Heterogeneous Large Language Models with Deep Parallel Collaboration](https://mlsanity.com/paper/2404.12715/) (2024)
- [BEST-Route: Adaptive LLM Routing with Test-Time Optimal Compute](https://mlsanity.com/paper/2506.22716/) (2025)
- [MixLLM: Dynamic Routing in Mixed Large Language Models](https://mlsanity.com/paper/2502.18482/) (2025)
- [Resourceful Contextual Bandits](https://mlsanity.com/paper/1402.6779/) (2014)
- [MetaLLM: A High-performant and Cost-efficient Dynamic Framework for Wrapping LLMs](https://mlsanity.com/paper/2407.10834/) (2024)
- [OmniRouter: Budget and Performance Controllable Multi-LLM Routing](https://mlsanity.com/paper/2502.20576/) (2025)
- [Algorithms with Logarithmic or Sublinear Regret for Constrained Contextual Bandits](https://mlsanity.com/paper/1504.06937/) (2015)
- [Adaptive LLM Routing under Budget Constraints](https://mlsanity.com/paper/2508.21141/) (2025)
- [Online Multi-LLM Selection via Contextual Bandits under Unstructured Context Evolution](https://mlsanity.com/paper/2506.17670/) (2025)
- [ThriftLLM: On Cost-Effective Selection of Large Language Models for Classification Queries](https://mlsanity.com/paper/2501.04901/) (2025)

## Built on by (most cited first, 3 of 3)

- [When Should Agents Check External State? Budgeting Observations for Stored Intentions](https://mlsanity.com/paper/2609.37125/) (2026)
- [Routing Should Pay for Itself: Sparse Supervision for Economical LLM Routing](https://mlsanity.com/paper/2609.37402/) (2026)
- [JOVE: Joint Execution and Verification for Resource-Aware LLM Task Graphs](https://mlsanity.com/paper/2610.03296/) (2026)

## Abstract (arXiv)

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.