# LLM-as-Judge on a Budget

arXiv: https://arxiv.org/abs/2602.15481 · HTML: https://mlsanity.com/paper/2602.15481/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 19 of its 29 references that are in the map.
- First posted on arXiv 17 Feb 2026.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 19 of 19)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [G-Eval: NLG Evaluation using GPT-4 with Better Human Alignment](https://mlsanity.com/paper/2303.16634/) (2023)
- [A Survey on LLM-as-a-Judge](https://mlsanity.com/paper/2411.15594/) (2024)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [AlpacaFarm: A Simulation Framework for Methods that Learn from Human Feedback](https://mlsanity.com/paper/2305.14387/) (2023)
- [Can Large Language Models Be an Alternative to Human Evaluations?](https://mlsanity.com/paper/2305.01937/) (2023)
- [Prometheus 2: An Open Source Language Model Specialized in Evaluating Other Language Models](https://mlsanity.com/paper/2405.01535/) (2024)
- [Is ChatGPT a Good NLG Evaluator? A Preliminary Study](https://mlsanity.com/paper/2303.04048/) (2023)
- [JudgeLM: Fine-tuned Large Language Models are Scalable Judges](https://mlsanity.com/paper/2310.17631/) (2023)
- [HelpSteer2: Open-source dataset for training top-performing reward models](https://mlsanity.com/paper/2406.08673/) (2024)
- [Judging the Judges: Evaluating Alignment and Vulnerabilities in LLMs-as-Judges](https://mlsanity.com/paper/2406.12624/) (2024)
- [When Scaling Meets LLM Finetuning: The Effect of Data, Model and Finetuning Method](https://mlsanity.com/paper/2402.17193/) (2024)
- [Repairing the Cracked Foundation: A Survey of Obstacles in Evaluation Practices for Generated Text](https://mlsanity.com/paper/2202.06935/) (2022)
- [Self-rationalization improves LLM as a fine-grained judge](https://mlsanity.com/paper/2410.05495/) (2024)
- [LLMEval: A Preliminary Study on How to Evaluate Large Language Models](https://mlsanity.com/paper/2312.07398/) (2023)
- [Fixed-Budget Best-Arm Identification with Heterogeneous Reward Variances](https://mlsanity.com/paper/2306.07549/) (2023)

## Built on by (most cited first, 5 of 5)

- [CyclicJudge: Mitigating Judge Bias Efficiently in LLM-based Evaluation](https://mlsanity.com/paper/2603.01865/) (2026)
- [Instance-Optimal Estimation with Multiple LLM Judges on a Budget](https://mlsanity.com/paper/2605.23362/) (2026)
- [Dynamically Allocating Evaluation Effort for Model Ranking](https://mlsanity.com/paper/2608.03437/) (2026)
- [Speculative Evaluation of Stochastic LLMs](https://mlsanity.com/paper/2609.28560/) (2026)
- [Are We Testing Too Much? A Survey of Benchmark Compression for Efficient Evaluation of Large Language Models](https://mlsanity.com/paper/2610.18248/) (2026)

## Abstract (arXiv)

LLM-as-a-judge has emerged as a cornerstone technique for evaluating large language models by leveraging LLM reasoning to score prompt-response pairs. Since LLM judgments are stochastic, practitioners commonly query each pair multiple times to estimate mean scores accurately. This raises a critical challenge: given a fixed computational budget B, how to optimally allocate queries across K prompt-response pairs to minimize estimation error? We present a principled variance-adaptive approach leveraging multi-armed bandit theory and concentration inequalities. Our method dynamically allocates queries based on estimated score variances, concentrating resources where uncertainty is highest. Further, our algorithm is shown to achieve a worst-case score-estimation error of tildeOleft(√fracsumi=1K σi2Bright), σi2 being the unknown score variance for pair i ∈ [K] with near-optimal budget allocation. Experiments on Summarize-From-Feedback and HelpSteer2 demonstrate that our method significantly outperforms uniform allocation, reducing worst-case estimation error while maintaining identical budgets. Our work establishes a theoretical foundation for efficient LLM evaluation with practical implications for AI safety, model alignment, and automated assessment at scale.