Knowing When to Stop: Bayesian Optimal Stopping for LLM Evaluations

The inherent rigidity of fixed-size benchmarks makes them an inefficient tool for model evaluation. Diverse evaluation objectives, including model ranking, model selection and testing throughout development, demand varying levels of statistical power. The mismatch between fixed sample sizes and these diverse needs results in either excessive computational cost or compromised reliability - a critical concern for model evaluation. To overcome these limitations, we call for adoption of sequential testing in our field. We provide an adaptive evaluation framework, that provides a principled way to navigate the trade-off between efficiency and reliability in model evaluation. Our framework combines the established statistical paradigm of sequential testing with stopping criteria tailored to common evaluation needs such as diminishing returns detection, and minimum detectable effect size. We demonstrate its ability to adaptively manage the efficiency-reliability trade-off on the Open VLM Leaderboard, including, for example, a 80% reduction in computational cost compared to fixed-size evaluation (with a 2.5-point CI width allowance) while maintaining statistical significance.

Evaluating a stochastic large language model is costly: benchmark scores estimate expected performance from randomized rollouts, yet uniform repetition ignores sharp differences in task-level rollout variance. We ask how to minimize the variance of a fixed-benchmark mean under an exact rollout budget. We develop Speculative Evaluation with a Hierarchical Bayesian Neyman (HBN) policy with pilot size and stage weight jointly chosen ex ante. It runs a short uniform pilot, pools per-task success counts with a hierarchical Bayesian model, and uses posterior expectations of task-level sampling variances for exact positive-integer Neyman allocation. To mitigate the pilot synchronization barrier, HBN-async speculatively executes continuations from partial pilot feedback and retains those selected by the final allocation. Across six checkpoints and 18 benchmark groups, we evaluate 107 nondegenerate benchmark-checkpoint profiles. For rollout budgets of 8-64 per task, Speculative Evaluation reduces variance relative to Uniform by 12.8%-33.6% on average across profiles, outperforming hindsight-tuned empirical and independent Bayesian baselines. Real-generation experiments that account for the pilot synchronization barrier show that HBN-async mitigates its overhead, helping translate statistical efficiency into practical evaluation benefits.

Can we trust evaluation scores to capture an LLM's true real-world performance? Certifiable evaluation answers this question by providing guarantee for LLM evaluation. In particular, existing methods sequentially curate evaluation samples and keep updating confidence intervals (CIs) that cover the true performance with high probability (e.g., 95%) until some conditions are satisfied, e.g., the CI width reaches a target precision. However, existing methods are not generally anytime-valid: the claimed coverage (e.g., 95%) may fail when CIs are repeatedly updated and used to decide when to stop, leaving a gap between theoretical rigor and practice. This paper bridges this gap by proposing Celeus, a Certifiable framework for Efficient LLM evaluation, which leverages E-processes to build anytime-valid CIs. Concretely, we propose signals that combine two ingredients: (i) Uncertainty-guided sampling to select informative samples for evaluation, and (ii) Surrogate-assisted approximations for unevaluated samples. We prove that such signals remain unbiased for the evaluation score conditional on the past, enabling statistically-grounded and anytime-valid $e$-process CIs. More importantly, the two ingredients reduce estimation variance and help reach the target precision with fewer evaluated samples. We also prove that CIs obtained by Celeus can shrink at a near-parametric rate up to logarithmic factors and analyze the oracle variance-optimal sampling rule that motivates the empirical uncertainty-guided one. Experiments show that Celeus reaches the target precision using 54-62% fewer evaluated samples than baselines, while preserving anytime-valid coverage.