[Paper Review] A Faithful Distributed Implementation of Dual Decomposition and Average Consensus Algorithms

Takashi Tanaka, Farhad Farokhi+1 more|arXiv (Cornell University)|Apr 10, 2013

Auction Theory and Applications15 references3 citations

TL;DR

This paper proposes a tax mechanism that incentivizes strategic agents to faithfully implement dual decomposition and average consensus algorithms in distributed networks, using a novel notion of asymptotic incentive compatibility. The mechanism ensures agents face diminishing incentives to deviate as the algorithm converges, enabling truthful implementation of asymptotic distributed optimization with private data.

ABSTRACT

We consider large scale cost allocation problems and consensus seeking problems for multiple agents, in which agents are suggested to collaborate in a distributed algorithm to find a solution. If agents are strategic to minimize their own individual cost rather than the global social cost, they are endowed with an incentive not to follow the intended algorithm, unless the tax/subsidy mechanism is carefully designed. Inspired by the classical Vickrey-Clarke-Groves mechanism and more recent algorithmic mechanism design theory, we propose a tax mechanism that incentivises agents to faithfully implement the intended algorithm. In particular, a new notion of asymptotic incentive compatibility is introduced to characterize a desirable property of such class of mechanisms. The proposed class of tax mechanisms provides a sequence of mechanisms that gives agents a diminishing incentive to deviate from suggested algorithm.

Motivation & Objective

• To address the challenge of ensuring truthful participation in distributed optimization when agents are strategic and self-interested.
• To design a mechanism that incentivizes agents to follow intended algorithms despite private information and individual cost minimization incentives.
• To extend classical mechanism design to asymptotic distributed algorithms like dual decomposition and average consensus.
• To formalize a new concept— asymptotic incentive compatibility—for sequences of mechanisms that reduce deviation incentives over time.
• To enable privacy-preserving, distributed computation of social decisions without requiring full data sharing.

Proposed method

• Introduces a tax mechanism inspired by the Vickrey-Clarke-Groves (VCG) mechanism, adapted for distributed, iterative algorithms.
• Designs a sequence of mechanisms where agents' incentives to deviate diminish as the algorithm approaches convergence.
• Uses a continuous-time approximation of the dual decomposition and consensus algorithms to model agent behavior and convergence.
• Applies the concept of ex-post Nash equilibrium to ensure that truthful reporting is optimal in the limit, even with private types.
• Employs a recursive update rule based on the gradient of the dual function and a consensus-based correction term to drive convergence.
• Defines a net cost function that combines individual cost and tax, ensuring rational agents minimize their total cost under the mechanism.

Experimental results

Research questions

• RQ1 How can a distributed optimization algorithm be implemented faithfully when agents are strategic and may misreport their private information?
• RQ2 What mechanism design principles can ensure that agents have diminishing incentives to deviate from the intended algorithm over time?
• RQ3 Can the VCG mechanism be generalized to work with asymptotic, iterative distributed algorithms like dual decomposition and average consensus?
• RQ4 How can privacy be preserved in distributed optimization while ensuring convergence to the socially optimal solution?
• RQ5 What conditions ensure that truthful reporting becomes asymptotically optimal in a sequence of mechanisms?

Key findings

• The proposed tax mechanism ensures asymptotic incentive compatibility, meaning agents have diminishing incentives to deviate as the algorithm progresses.
• The mechanism is a generalization of the VCG mechanism tailored for iterative, distributed algorithms with private data.
• Convergence to the optimal solution is guaranteed under the mechanism, even when agents act strategically.
• The limit of the algorithm output satisfies feasibility, and the net cost of truthful reporting is minimized in the long run.
• The framework allows distributed computation without requiring agents to disclose their private information.
• Theoretical analysis proves that truthful reporting is optimal in ex-post Nash equilibria for the sequence of mechanisms.