# Which LLM for Which Work? Budgeted Model Allocation under Uncertain Evaluation

arXiv: https://arxiv.org/abs/2608.29560 · HTML: https://mlsanity.com/paper/2608.29560/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 34 references that are in the map.
- First posted on arXiv 30 Aug 2026.

## Builds on (most cited first, 24 of 24)

- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [A Survey on LLM-as-a-Judge](https://mlsanity.com/paper/2411.15594/) (2024)
- [Chatbot Arena: An Open Platform for Evaluating LLMs by Human Preference](https://mlsanity.com/paper/2403.04132/) (2024)
- [Large Language Models are not Fair Evaluators](https://mlsanity.com/paper/2305.17926/) (2023)
- [LLM Evaluators Recognize and Favor Their Own Generations](https://mlsanity.com/paper/2404.13076/) (2024)
- [RouterBench: A Benchmark for Multi-LLM Routing System](https://mlsanity.com/paper/2403.12031/) (2024)
- [HelpSteer2: Open-source dataset for training top-performing reward models](https://mlsanity.com/paper/2406.08673/) (2024)
- [Prediction-Powered Inference](https://mlsanity.com/paper/2301.09633/) (2023)
- [GraphRouter: A Graph-based Router for LLM Selections](https://mlsanity.com/paper/2410.03834/) (2024)
- [Measuring what Matters: Construct Validity in Large Language Model Benchmarks](https://mlsanity.com/paper/2511.04703/) (2025)
- [SWE-Lancer: Can Frontier LLMs Earn 1 Million from Real-World Freelance Software Engineering?](https://mlsanity.com/paper/2502.12115/) (2025)
- [KuaiRand: An Unbiased Sequential Recommendation Dataset with Randomly Exposed Videos](https://mlsanity.com/paper/2208.08696/) (2022)
- [Router-R1: Teaching LLMs Multi-Round Routing and Aggregation via Reinforcement Learning](https://mlsanity.com/paper/2506.09033/) (2025)
- [Position: Evaluating Generative AI Systems Is a Social Science Measurement Challenge](https://mlsanity.com/paper/2502.00561/) (2025)
- [AutoEval Done Right: Using Synthetic Data for Model Evaluation](https://mlsanity.com/paper/2403.07008/) (2024)
- [Limits to scalable evaluation at the frontier: LLM as Judge won't beat twice the data](https://mlsanity.com/paper/2410.13341/) (2024)
- [LLMRouterBench: A Massive Benchmark and Unified Framework for LLM Routing](https://mlsanity.com/paper/2601.07206/) (2026)
- [Causal LLM Routing: End-to-End Regret Minimization from Observational Data](https://mlsanity.com/paper/2505.16037/) (2025)
- [CP-Router: An Uncertainty-Aware Router Between LLM and LRM](https://mlsanity.com/paper/2505.19970/) (2025)
- [DiSRouter: Distributed Self-Routing for LLM Selections](https://mlsanity.com/paper/2510.19208/) (2025)
- [Optimal Verification of a Minimum-Weight Basis in an Uncertainty Matroid](https://mlsanity.com/paper/2512.17116/) (2025)
- [Budgeted Active Experimentation for Treatment Effect Estimation from Observational and Randomized Data](https://mlsanity.com/paper/2602.22021/) (2026)
- [Causal methods for LLM development and evaluation](https://mlsanity.com/paper/2605.25998/) (2026)
- [Meta-Router: Bridging Gold-standard and Preference-based Evaluations in Large Language Model Routing](https://mlsanity.com/paper/2509.25535/) (2025)

## Abstract (arXiv)

A company with a fixed artificial intelligence (AI) budget must decide which large language model (LLM) handles each recurring workload. What it lacks is the quality table, how well each model performs on each workload. Given that table, the decision is a multiple-choice knapsack problem and is routine to solve, so estimating it is the difficulty, and that estimation fails in two ways. Models are rarely compared on the same work, and the recorded score is usually a proxy rather than the outcome the company values. Causal and off-policy methods repair the first but condition on the second, while evaluator-validation methods estimate the second but stop short of the decision. Worse, buying more re-evaluation cannot settle the second: randomization governs which requests are scored, not how a score is produced, so the table stays uncertain however much evaluation is purchased. Yet the deployment decision may still be determined even when the table is not. We therefore ask whether one assignment stays optimal across every quality table consistent with the evidence. For the fixed-budget problem, this admits an exact two-solve certificate: solve once at the estimated table and once at a least-favourable table. Agreement certifies the assignment; disagreement identifies the model-workload pairs where further evidence can matter. We propose CASE (causal active sequential experimentation), which targets evaluation to those pairs and repeats the test as evidence accumulates. On a production log, the measurement failure is the larger of the two: correcting assignment exactly still leaves most of the loss, and randomized re-evaluation does not remove it. In our experiments, the available evidence often does not determine the assignment. On paid software tasks, better information about model quality yields more savings than further optimization of the assignment on the same estimates.