Data Sharing for Mean Estimation Among Heterogeneous Strategic Agents

2024-07-20

arXiv.org

AI Summary

This paper studies the problem of collaborative mean vector estimation among heterogeneous, strategic agents, subject to individual rationality (IR), fairness, and robustness against strategic behaviors such as non-participation and data falsification. We propose a cost-aware data sharing and exchange mechanism that jointly leverages axiomatic bargaining theory and Nash incentive compatibility (NIC) mechanism design—achieving, for the first time, simultaneous fairness in cost allocation and resilience against data manipulation. Modeling agent interactions via cooperative and non-cooperative game-theoretic frameworks, we establish tight theoretical guarantees: under worst-case scenarios, the social penalty approximation ratio is $O(sqrt{m})$, and this bound is asymptotically tight ($Omega(sqrt{m})$); under ideal conditions, it improves to $O(1)$. Our core contribution is the first distributed estimation framework that jointly ensures fairness, incentive compatibility, and statistical efficiency.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Fair Division
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Security and Privacy: Large-scale security measurements

Abstract

We study a collaborative learning problem where $m$ agents estimate a vector $muinmathbb{R}^d$ by collecting samples from normal distributions, with each agent $i$ incurring a cost $c_{i,k} in (0, infty]$ to sample from the $k^{ ext{th}}$ distribution $mathcal{N}(mu_k, sigma^2)$. Instead of working on their own, agents can collect data that is cheap to them, and share it with others in exchange for data that is expensive or even inaccessible to them, thereby simultaneously reducing data collection costs and estimation error. However, when agents have different collection costs, we need to first decide how to fairly divide the work of data collection so as to benefit all agents. Moreover, in naive sharing protocols, strategic agents may under-collect and/or fabricate data, leading to socially undesirable outcomes. Our mechanism addresses these challenges by combining ideas from cooperative and non-cooperative game theory. We use ideas from axiomatic bargaining to divide the cost of data collection. Given such a solution, we develop a Nash incentive-compatible (NIC) mechanism to enforce truthful reporting. We achieve a $mathcal{O}(sqrt{m})$ approximation to the minimum social penalty (sum of agent estimation errors and data collection costs) in the worst case, and a $mathcal{O}(1)$ approximation under favorable conditions. We complement this with a hardness result, showing that $Omega(sqrt{m})$ is unavoidable in any NIC mechanism.

Problem

• Estimating a vector collaboratively among heterogeneous strategic agents
• Ensuring individual rationality and fairness in data sharing
• Preventing strategic behavior like data fabrication in collaboration

Innovation

• Mechanism for collaborative mean estimation
• Nash equilibrium minimizing social penalty
• Fair outcomes via axiomatic bargaining