Towards Reliable LLM Evaluation: Correcting the Winner's Curse in Adaptive Benchmarking

Efficient benchmarking techniques aim to lower the computational cost of evaluating LLMs by predicting full benchmark scores using only a subset of a benchmark's questions. By reframing this problem as an instance of multiple regression with feature selection, we find that existing efficient benchmarking methods can be greatly improved by simply using kernel ridge regression at the prediction stage. Additionally, using an information-theoretic feature-selection algorithm called minimum redundancy maximum relevance (mRMR), we can further improve upon these methods by selecting question subsets that will be maximally useful for prediction. Except in very data-poor settings, these approaches consistently achieve smaller prediction errors (in both MAE and RMSE), and greater ranking correlation between predicted and true scores (in both Spearman $ρ$ and Kendall $τ$) across a range of benchmarks using both binary and continuous metrics. Furthermore, mRMR subsampling is much faster than competitor methods (which often involve fitting probabilistic models or running clustering algorithms), and is more likely to select the same questions under different random seeds or training data splits. Tutorial code can be found at https://github.com/sambowyer/mrmr_eval .

Exhaustively evaluating every candidate LLM configuration on every benchmark item to identify a high-performing one is costly. We formulate configuration selection as a cost-aware Bayesian bandit problem and propose GittinsEval, which draws on the Bayesian-optimal Gittins policy to determine which configuration to evaluate next and when to stop. We extend the policy with an anytime recommendation rule over both fully and partially evaluated configurations, using an LCB-style score to account for posterior uncertainty. GittinsEval is computationally efficient, requiring only lightweight online updates after offline precomputation. Across GSM8K, PIQA, AlpacaEval, and MMLU response matrices, GittinsEval is consistently competitive, with particularly strong gains over configuration-level Bayesian optimization on large-example benchmarks and over cost-unaware bandit baselines on large-candidate tasks. Crucially, GittinsEval often attains near-zero simple regret using only 1% to 2% of the exhaustive-evaluation cost; it also offers an adaptive stopping rule that typically triggers at 1% to 10%.

Selecting the best large language model (LLM) for a fixed benchmark is often expensive, since exhaustive evaluation requires running every model on every example. Multi-armed bandit (MAB) algorithms can reduce the number of LLM calls by sequentially selecting the next model-example pair to evaluate, thereby avoiding wasted evaluations on clearly underperforming models. Further savings can be achieved by predicting model scores from the partially observed model-example score matrix using low-rank factorization. However, such predictions are not ground truth: they can be biased and may therefore lead to incorrect identification of the best model. In this work, we propose a principled framework that combines MAB with cheap predicted scores without compromising statistical validity. Specifically, we derive doubly robust estimators of each model's performance that use the low-rank predictions to reduce variance. This enables the construction of valid finite-sample confidence intervals in our setting, where models are selected adaptively and examples are sampled without replacement. Empirical results on real-world benchmarks show that our approach reduces the number of required evaluations, yielding meaningful savings in compute and cost while accurately identifying the best-performing model.