Iyer et al. model two-stage pricing for AI training with uncertain outcomes

A new academic paper from Krishnamurthy Iyer, Alec Sun, Haifeng Xu, and You Zu tackles the challenge of pricing services with uncertain outcomes, such as machine learning training where model performance varies. The authors propose a two-stage payment scheme: an upfront fee plus outcome-dependent usage prices. After the buyer pays the upfront and sees the realized quality, they can accept (pay usage price) or reject (no further payment). The paper proves that this structure is necessary for profit maximization—using only upfront or only usage prices is insufficient.

On computational complexity, the team shows that finding the optimal profit is NP-hard even with just two buyer types. However, they develop a fully-polynomial time approximation scheme (FPTAS) for a constant number of buyer types, enabling near-optimal pricing in practice. Additionally, in a single-parameter setting where buyer valuations depend on one real number, they prove that a revenue-optimal menu contains just a single contract. This work provides a rigorous foundation for pricing AI training services, giving providers clear strategies to balance risk and revenue.