Mechanism Design for LLM Fine-tuning with Multiple Reward Models

Fine-tuning large language models (LLMs) to aggregate multiple preferences has attracted considerable research attention. With aggregation algorithms advancing, a potential economic scenario arises where fine-tuning services are provided to agents with different preferences. In this context, agents may benefit from strategically misreporting their preferences, which could affect the fine-tuned outcomes. This paper addresses such incentive issues by framing it as a mechanism design problem: an LLM provider determines the fine-tuning objective (training rule) and the pricing scheme (payment rule) for agents. We primarily focus on a representative class of training rules that maximize social welfare subject to certain regularizations, referred to as \tr\ rules. Firstly, we show that under most circumstances, truthful reporting is sub-optimal with simply a training rule, thereby highlighting the necessity of payments. Secondly, we design affine maximizer payment rules that implement \tr\ rules in dominant-strategy incentive compatibility (DSIC). We characterize sufficient conditions for payment equivalence properties. For a training rule that satisfies these conditions, we have found all the payment rules that implement it in DSIC, as they only differ by a constant term irrelevant to agents' reports from each other. Thirdly, we demonstrate that our mechanism is approximately DSIC even with perturbed input, showcasing its robustness against the inevitable errors in real-world applications. Experiments on real LLM setups further confirm the practical implications of our results.