Abstract
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, focusing resources where uncertainty is highest. Our algorithm is shown to achieve a worst-case score-estimation error of Õ(√(∑_i=1^K σ_i^2/B)), σ_i^2 being the unknown score variance for pair i ∈ [K] with near-optimal budget allocation. Experiments on HelpSteer2 dataset demonstrate our method significantly outperforms uniform allocation, reducing worst-case estimation error given a fixed budget. Our work establishes a theoretical foundation for efficient LLM evaluation with practical implications for AI safety, model alignment, and automated assessment at scale.