Utility-Aware Data Pricing: Token-Level Quality and Empirical Training Gain for LLMs

Scaling LLMs requires tremendous computational resources, and recent advances in AI have gone hand in hand with massive amounts of capital expenditure. While it is established that scaling up LLMs reliably increases model quality (quantified in terms of loss or downstream evaluations), it is unclear how these quality improvements translate to potential revenue, and whether revenue increases would offset costs of larger-scale training and inference. In this work, we develop an economic model for characterizing the rational behavior of an LLM training firm by combining scaling laws with microeconomic theory. Under our model of firm behavior, LLM quality can be increased with more parameters and training tokens, leading to more potential adoption by consumers, who each have a quality threshold for using the LLM. On the other hand, additional parameters and training tokens both incur additional costs. We analyze the profit maximization problem for this model under compute-bound and data-bound regimes. In the compute-bound regime, optimal model size and token budget track hardware efficiency $E$ (FLOPs/$) at a near-linear rate; total training cost then scales sub-quadratically in $E$. Data efficiency improvements incentivize larger models and training expenditure. When we are limited to $D$ data, profit-optimal training expenditure scales as $D^2/E$, i.e, increase with data and decreases with hardware efficiency (as well as data efficiency). Finally, we analyze practical trends in training expenditure: current trends are consistent with our most permissive model variants in the compute-bound regime, but are not profit-optimal in the data-bound regime or assuming hardware advances will stall. Overall, our results provide a theory of profit-optimal LLM training, providing a foundation for engaging critically with industry statements and supporting long-term economic decision making.

Data valuation is a natural framework for understanding which preference datasets matter most when aligning a Large Language Model (LLM) using multiple sources. The standard game-theoretic approach assigns each dataset a contribution score via the Shapley value. In practice, however, Shapley-based valuation is computationally prohibitive because it requires fine-tuning a separate model for every possible coalition of preference datasets, i.e., an exponential number of alignments. We address this challenge for a broad family of preference-optimization objectives, including DPO and IPO, that learn directly from log-policy ratios with respect to a reference policy. We introduce Sequential Preference Optimization, an offline procedure that applies existing preference optimization methods sequentially, source by source, updating the current policy after each dataset. Under exact optimization, this procedure yields an additive composition rule in reward space and an equivalent arithmetic composition rule in policy space. This observation enables an efficient approximation of the Shapley value: we train one model per preference dataset and reconstruct coalition policies at inference time from the singleton models, reducing the required alignments from exponential to linear in the number of sources. Leveraging this property, we compute Shapley values for several real-world preference datasets and reveal how each source drives model alignment.

Improving LLM performance on downstream tasks sometimes requires leveraging auxiliary datasets during post-training. In practice, however, developers face constraints on compute, labeling, and licensing costs that preclude using all available data, necessitating principled dataset-level selection. These constraints are increasingly shaped by dataset marketplaces, where data acquisition is governed by budgets and negotiation. We study dataset valuation as a subset selection problem during LLM post-training. Our goal is to identify and weight auxiliary datasets so as to maximize target task performance given constrained budgets. We first show that commonly used gradient alignment scores provide a reasonable yet incomplete valuation signal, as they ignore redundancy among datasets. To address this, we propose a scalable convex dataset-level valuation method based on kernel mean matching (KMM) in gradient space, which jointly accounts for alignment with the target task and redundancy across auxiliary datasets. Through extensive experiments across diverse post-training settings and tasks, we show that our approach consistently outperforms existing valuation baselines, achieving stronger performance with low computational overhead. Our results position dataset valuation as a practical decision tool for post-training data selection in market-constrained large language model settings. The code is available at https://github.com/uiuctml/convex_data_valuation.