Designing Service Systems from Textual Evidence

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.

[Abridged] Production LLM deployments receive feedback from a non-random fraction of users: thumbs sit mostly in the tails of the satisfaction distribution, and a naive average over them can land 40-50 percentage points away from true system quality. We treat this as a topic- and sentiment- stratified selection-bias problem and propose a three-agent hierarchical Bayesian pipeline that does not require ground-truth labels on individual interactions. A Topic Clustering Agent partitions the stream via UMAP + HDBSCAN over text embeddings; a Bias Modeling Agent fits a two-stage hierarchical Beta-Binomial under NUTS, inferring per-topic selection rates $s_c$ and quality $q_c$ with partial pooling; a Synthesis Agent reweights $q_c$ by true topic prevalence $\hatπ_c = n_c/N$ to report a bias-corrected aggregate posterior $\bar Q = \sum_c \hatπ_c q_c$ with credible interval, plus drift signals for online recalibration. Validation uses UltraFeedback (N=10,232 retained interactions, $C=18$ clusters, $Q^\star=0.6249$) with simulated topic- and sentiment-dependent selection biases. We compare five Bayesian variants against Naive and IPW baselines. A mild prior on the feedback channel (typical positive-feedback rate and negative-to-positive ratio, both readable from any production dashboard without labels) keeps Hierarchical-Informed within 4-13 pp of $Q^\star$ as the bias ratio sweeps from 1:1 to 30:1, with 95% credible intervals covering $Q^\star$ in 50/50 random-seed replicates at $κ_{\max}=10$. Without channel-side priors, every weak-prior variant misses $Q^\star$ by 22-33 pp: the per-cluster sufficient statistics admit a one-parameter family of equally good fits, and the prior on the bias channel (not on latent quality) is what breaks the degeneracy.

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 $\tilde{O}\left(\sqrt{\frac{\sum_{i=1}^K σ_i^2}{B}}\right)$, $σ_i^2$ being the unknown score variance for pair $i \in [K]$ 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.