# Online Prompt Pricing based on Combinatorial Multi-Armed Bandit and Hierarchical Stackelberg Game

arXiv: https://arxiv.org/abs/2405.15154 · HTML: https://mlsanity.com/paper/2405.15154/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 42 references that are in the map.
- First posted on arXiv 24 May 2024.

## Builds on (most cited first, 15 of 15)

- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [CLIPScore: A Reference-free Evaluation Metric for Image Captioning](https://mlsanity.com/paper/2104.08718/) (2021)
- [Exploring CLIP for Assessing the Look and Feel of Images](https://mlsanity.com/paper/2207.12396/) (2022)
- [A Principled Approach to Data Valuation for Federated Learning](https://mlsanity.com/paper/2009.06192/) (2020)
- [A Marketplace for Data: An Algorithmic Solution](https://mlsanity.com/paper/1805.08125/) (2018)
- [Prompt Stealing Attacks Against Text-to-Image Generation Models](https://mlsanity.com/paper/2302.09923/) (2023)
- [Model-based Pricing for Machine Learning in a Data Marketplace](https://mlsanity.com/paper/1805.11450/) (2018)
- [Improving Fairness for Data Valuation in Horizontal Federated Learning](https://mlsanity.com/paper/2109.09046/) (2021)
- [Data Pricing in Machine Learning Pipelines](https://mlsanity.com/paper/2108.07915/) (2021)
- [A Marketplace for Trading AI Models based on Blockchain and Incentives for IoT Data](https://mlsanity.com/paper/2112.02870/) (2021)
- [Optimized, Direct Sale of Privacy in Personal-Data Marketplaces](https://mlsanity.com/paper/1701.00740/) (2017)
- [Online Pricing with Reserve Price Constraint for Personal Data Markets](https://mlsanity.com/paper/1911.12598/) (2019)
- [Semi-Private Computation of Data Similarity with Applications to Data Valuation and Pricing](https://mlsanity.com/paper/2206.06650/) (2022)

## Abstract (arXiv)

Generation models have shown promising performance in various tasks, making trading around machine learning models possible. In this paper, we aim at a novel prompt trading scenario, prompt bundle trading (PBT) system, and propose an online pricing mechanism. Based on the combinatorial multi-armed bandit (CMAB) and three-stage hierarchical Stackelburg (HS) game, our pricing mechanism considers the profits of the consumer, platform, and seller, simultaneously achieving the profit satisfaction of these three participants. We break down the pricing issue into two steps, namely unknown category selection and incentive strategy optimization. The former step is to select a set of categories with the highest qualities, and the latter is to derive the optimal strategy for each participant based on the chosen categories. Unlike the existing fixed pricing mode, the PBT pricing mechanism we propose is more flexible and diverse, which is more in accord with the transaction needs of real-world scenarios. We test our method on a simulated text-to-image dataset. The experimental results demonstrate the effectiveness of our algorithm, which provides a feasible price-setting standard for the prompt marketplaces.