Collaborative machine learning enables multiple data owners to jointly train models for improved predictive performance. However, ensuring incentive compatibility and fair contribution-based rewards remains a critical challenge. Prior work by Sim and colleagues (Rachel Hwee Ling Sim et al: Collaborative machine learning with incentive-aware model rewards. In: International conference on machine learning. PMLR. 2020, pp. 8927-8963) addressed this by allocating model rewards, which are non-monetary and freely replicable, based on the Shapley value of each party's data contribution, measured via information gain. In this paper, we introduce a ratio-based Shapley value that replaces the standard additive formulation with a relative contribution measure. While our overall reward framework, including the incentive definitions and model-reward setting, remains aligned with that of Sim and colleagues, the underlying value function is fundamentally different. Our alternative valuation induces a different distribution of model rewards and offers a new lens through which to analyze incentive properties. We formally define the ratio-based value and prove that it satisfies the same set of incentive conditions as the additive formulation, including adapted versions of fairness, individual rationality, and stability. Like the original approach, our method faces the same fundamental trade-offs between these incentives. Our contribution is a mathematically grounded alternative to the additive Shapley framework, potentially better suited to contexts where proportionality among contributors is more meaningful than additive differences.

翻译：协作机器学习允许多个数据所有者联合训练模型以提高预测性能。然而，确保激励兼容性和基于贡献的公平奖励分配仍是一个关键挑战。Sim及其同事先前的研究（Rachel Hwee Ling Sim等人：《具有激励感知模型奖励的协作机器学习》，载于：国际机器学习会议，PMLR，2020年，第8927-8963页）通过基于各方数据贡献的Shapley值（通过信息增益衡量）来分配模型奖励（非货币性且可自由复制），从而解决了这一问题。本文提出了一种基于比率的Shapley值，用相对贡献度量替代了标准的加性公式。尽管我们的整体奖励框架（包括激励定义和模型奖励设置）仍与Sim等人的研究保持一致，但基础价值函数存在本质差异。这种替代性估值方式导致了模型奖励的不同分布，并为分析激励特性提供了新的视角。我们正式定义了基于比率的价值函数，并证明其满足与加性公式相同的激励条件集合，包括适应性版本的公平性、个体理性与稳定性。与原始方法类似，我们的方法同样面临这些激励之间的根本性权衡。本研究的贡献在于为加性Shapley框架提供了一个数学上严谨的替代方案，该方案可能更适用于贡献者间比例关系比加性差异更具意义的应用场景。