Collaborative machine learning (CML) provides a promising paradigm for democratizing advanced technologies by enabling cost-sharing among participants. However, the potential for rent-seeking behaviors among parties can undermine such collaborations. Contract theory presents a viable solution by rewarding participants with models of varying accuracy based on their contributions. However, unlike monetary compensation, using models as rewards introduces unique challenges, particularly due to the stochastic nature of these rewards when contribution costs are privately held information. This paper formalizes the optimal contracting problem within CML and proposes a transformation that simplifies the non-convex optimization problem into one that can be solved through convex optimization algorithms. We conduct a detailed analysis of the properties that an optimal contract must satisfy when models serve as the rewards, and we explore the potential benefits and welfare implications of these contract-driven CML schemes through numerical experiments.

翻译：协作机器学习（CML）通过实现参与者之间的成本分摊，为先进技术的民主化提供了一种前景广阔的范式。然而，各方潜在的寻租行为可能破坏此类协作。合约理论提供了一种可行的解决方案，即根据参与者的贡献，奖励他们不同准确度的模型。然而，与货币补偿不同，使用模型作为奖励带来了独特的挑战，尤其是在贡献成本为私有信息时，这些奖励具有随机性。本文形式化了CML中的最优合约设计问题，并提出了一种转换方法，将非凸优化问题简化为可通过凸优化算法求解的问题。我们详细分析了以模型作为奖励时最优合约必须满足的性质，并通过数值实验探讨了这些合约驱动的CML方案的潜在收益与福利影响。