Collaborative machine learning allows multiple data owners to jointly train models for improved predictive performance, but designing fair, incentive-compatible rewards remains challenging. Sim et al. [9] addressed this by distributing non-monetary, replicable model rewards based on each participant’s additive Shapley value, reflecting their information contribution. We introduce a ratio-based Shapley value, which measures relative rather than absolute contributions. While our framework remains aligned with Sim et al., the underlying value function differs, producing a distinct reward distribution and offering a new perspective on incentives. We formally define the ratio-based value and prove it satisfies the same conditions as the additive formulation, including adapted fairness, individual rationality, and stability. Like the original scheme, it faces the same trade-offs between incentives, but it provides a mathematically grounded alternative that may better suit contexts where proportional contributions are more meaningful than absolute gains.

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A Ratio-Based Shapley Value for Collaborative Machine Learning

  • Björn Filter,
  • Ralf Möller,
  • Özgür Lütfü Özçep

摘要

Collaborative machine learning allows multiple data owners to jointly train models for improved predictive performance, but designing fair, incentive-compatible rewards remains challenging. Sim et al. [9] addressed this by distributing non-monetary, replicable model rewards based on each participant’s additive Shapley value, reflecting their information contribution. We introduce a ratio-based Shapley value, which measures relative rather than absolute contributions. While our framework remains aligned with Sim et al., the underlying value function differs, producing a distinct reward distribution and offering a new perspective on incentives. We formally define the ratio-based value and prove it satisfies the same conditions as the additive formulation, including adapted fairness, individual rationality, and stability. Like the original scheme, it faces the same trade-offs between incentives, but it provides a mathematically grounded alternative that may better suit contexts where proportional contributions are more meaningful than absolute gains.