LEAP: Learning-Dynamics-Guided Open-Loop Pricing for LLM Data Acquisition

Abstract

The sustainability of AI-powered Web platforms often relies on a feedback loop: stronger models improve user experience, which can help generate interaction data for further refinement. During Large Language Model (LLM) fine-tuning, however, the marginal utility of additional data can change over time, while many incentive mechanisms are primarily reactive. For example, contextual-bandit approaches treat training as a black box and adjust payments only after observing stochastic feedback, which makes it difficult to plan budgets ex ante or to communicate a stable pricing plan. We introduce LEAP (Learning-dynamics-based Economic Adaptive Pricing), a framework that formulates data acquisition as an open-loop planning problem guided by a simple proxy of learning dynamics. Specifically, LEAP links an analytically motivated approximation of SGD progress to a Stackelberg-style pricing model, and yields a closed-form, deterministic price schedule that can be computed before training starts. The resulting schedule is transparent and easy to interpret, and serves as a structured baseline for aligning economic spending with longer-horizon training objectives in commitment-sensitive settings. Across controlled market-simulator experiments in three domains (Medical, Finance, and Comprehension), LEAP achieves lower evaluated acquisition-cost objectives than representative heuristic and online-learning baselines in many tested settings, with reductions exceeding 30% in representative long-horizon configurations. We further evaluate sensitivity to deviations from idealized assumptions, including non-linear supply curves and heterogeneous noise patterns, and find that the planned schedules remain competitive in the simulated settings considered. Overall, LEAP provides a planning-oriented starting point for integrating coarse learning-curve priors into interpretable pricing design for LLM data collection.