LMaaS: Exploring Pricing Strategy of Large Model as a Service for Communication

TL;DR

This work introduces Large Model as a Service (LMaaS) for semantic communication, where service providers price and rent multimodal large models to heterogeneous and dynamic clients. The market is modeled as a two-step Stackelberg game: a seller optimizes model pricing via Iterative Model Pricing (IMP), and customers solve a two-stage robust problem using Robust Selecting and Renting (RSR) to decide model choices and rental durations under uncertainty. The authors prove convergence and optimality properties for the proposed algorithms and demonstrate substantial gains: RSR yields up to 43.96% profit improvements for customers under varying conditions, while IMP achieves near-optimal seller profits with significant time savings. Collectively, the results validate LMaaS as a robust, scalable pricing framework for intelligent communication systems and highlight its practical potential for deploying foundation models across diverse, real-world environments.

Abstract

The next generation of communication is envisioned to be intelligent communication, that can replace traditional symbolic communication, where highly condensed semantic information considering both source and channel will be extracted and transmitted with high efficiency. The recent popular large models such as GPT4 and the boosting learning techniques lay a solid foundation for the intelligent communication, and prompt the practical deployment of it in the near future. Given the characteristics of "training once and widely use" of those multimodal large language models, we argue that a pay-as-you-go service mode will be suitable in this context, referred to as Large Model as a Service (LMaaS). However, the trading and pricing problem is quite complex with heterogeneous and dynamic customer environments, making the pricing optimization problem challenging in seeking on-hand solutions. In this paper, we aim to fill this gap and formulate the LMaaS market trading as a Stackelberg game with two steps. In the first step, we optimize the seller's pricing decision and propose an Iterative Model Pricing (IMP) algorithm that optimizes the prices of large models iteratively by reasoning customers' future rental decisions, which is able to achieve a near-optimal pricing solution. In the second step, we optimize customers' selection decisions by designing a robust selecting and renting (RSR) algorithm, which is guaranteed to be optimal with rigorous theoretical proof. Extensive experiments confirm the effectiveness and robustness of our algorithms.

Figures (14)

• Figure 1: The multimodal semantic communication workflow.
• Figure 2: The semantic communication market includes a seller and multiple customers. Seller prices different semantic communication models and customers decide model selection and rent duration.
• Figure 3: The training description of multimodal large language models, consisting of four parts: self-supervised learning, supervised fine-tuning, reward modeling, and reinforcement learning.
• Figure 4: Profit of customers with different # of customers
• Figure 5: Profit of customers with different # of SC models

Theorems & Definitions (3)

• Definition 1: Stackelberg Equilibrium
• Proposition 1
• Proposition 2