Paid with Models: Optimal Contract Design for Collaborative Machine Learning

2024-12-15

AI Summary

To address unobservable contributions and unfair reward allocation in collaborative machine learning (CML) arising from participants’ private training costs, this paper pioneers modeling model accuracy as a stochastic non-monetary reward and formalizes an optimal incentive mechanism grounded in contract theory. We propose a novel non-convex-to-convex equivalent transformation that preserves theoretical optimality while enabling efficient computation. Integrating Bayesian mechanism design with stochastic performance analysis, we rigorously derive the structural properties of the optimal contract. Numerical experiments demonstrate that our mechanism significantly reduces rent dissipation and improves social welfare by 23.6%, while guaranteeing strong incentive compatibility. The core contribution is the first computationally tractable framework for designing optimal contracts in CML where model performance serves as the reward—bridging contract theory with practical federated learning incentives.

Technology Category

• Multiagent Systems: Mechanism Design
• Machine Learning: Distributed Machine Learning & Federated Learning
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

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.

Problem

• Collaborative Machine Learning
• Optimal Contract Design
• Reward Uncertainty

Innovation

• Collaborative Machine Learning
• Optimal Contract Design
• Model-as-Reward Uncertainty