Paid with Models: Optimal Contract Design for Collaborative Machine Learning

TL;DR

This paper develops an optimal contract framework for collaborative machine learning where models, rather than money, are used as rewards, addressing the challenges of private contribution costs and stochastic outcomes.

Contribution

It formalizes the optimal contracting problem in CML with model rewards and introduces a transformation to solve the non-convex optimization efficiently.

Findings

Optimal contracts can be characterized by specific properties.

Transformations enable convex optimization solutions.

Contract schemes improve welfare in CML settings.

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.