A VCG-based Fair Incentive Mechanism for Federated Learning

TL;DR

This paper presents a VCG-based FL incentive mechanism, named FVCG, specifically designed for incentivizing data owners to contribute all their data and truthfully report their costs in FL settings, which maximizes the social surplus and minimizes unfairness of the federation.

Abstract

The enduring value of the Vickrey-Clarke-Groves (VCG) mechanism has been highlighted due to its adoption by Facebook ad auctions. Our research delves into its utility in the collaborative virtual goods production (CVGP) game, which finds application in realms like federated learning and crowdsourcing, in which bidders take on the roles of suppliers rather than consumers. We introduce the Procurement-VCG (PVCG) sharing rule into existing VCG mechanisms such that they can handle capacity limits and the continuous strategy space characteristic of the reverse auction setting in CVGP games. Our main theoretical contribution provides mathematical proofs to show that PVCG is the first in the CVGP game context to simultaneously achieve truthfulness, Pareto efficiency, individual rationality, and weak budget balance. These properties suggest the potential for Pareto-efficient production in the digital planned economy. Moreover, to compute the PVCG payments in a noisy economic environment, we propose the Report-Interpolation-Maximization (RIM) method. RIM facilitates the learning of the optimal procurement level and PVCG payments through iterative interactions with suppliers.

Figures (9)

• Figure 1: Circular flow diagram of Web-driven collaborative virtual goods production and consumption.
• Figure 2: Circular flow diagram of classical economy.
• Figure 3: Report-Interpolation-Maximization iteration.
• Figure 4: Experimental design.
• Figure 5: Trajectory of the RIM iteration. Diamond markers highlight the values obtained from the closed-form solution (addressing RQ1).

Theorems & Definitions (15)

• Proposition 1: Dominant-strategy incentive compatibility on the supply side
• Theorem 1: Crémer-McLean Theorem cremer-mclean-creemer1985optimalmcafee1992correlatedkosenok2008individually
• Corollary 1
• proof
• Proposition 2: Pareto efficiency
• Proposition 3: Ex-post individual rationality
• Proposition 4: Ex-post weak budget balance
• Proposition 5: PVCG with Interpolated Curves
• Theorem 2: The First Theorem of Welfare Economics
• proof : Dominant-Strategy Incentive Compatibility