Tight Efficiency Guarantees for Strategyproof Linear Regression

2026-09-27

AI Summary

This study addresses the fundamental trade-off between prediction accuracy and incentive compatibility in linear regression, tackling the challenge of truthful reporting under privacy-preserving labels. By integrating mechanism design, game theory, and optimization algorithms, this work constructs deterministic group strategy-proof mechanisms and systematically investigates theoretical bounds under various loss functions. The contributions resolve pertinent open questions by revealing sharp separation bounds. Specifically, it achieves a (d+1)-approximation optimal ratio and establishes a tight bound of 2−1/(⌈d/2⌉+1) for absolute loss, thereby completing a significant theoretical breakthrough in this research direction.

Abstract

We study the trade-off between squared-error accuracy and incentive compatibility in linear regression. Agents report private labels associated with publicly known features and prefer predictions close to their true labels. Ordinary least squares (OLS) need not elicit truthful reports. For regression with $d$ parameters, we design a deterministic group-strategyproof mechanism achieving a $(d+1)$-approximation to the least-squares optimum and prove optimality even among universally strategyproof randomized mechanisms, answering an open question of Chen et al. (EC 2018). Relaxing universal strategyproofness to strategyproofness in expectation reveals a sharp separation: squared individual loss retains the factor $d+1$, while absolute individual loss admits the tight ratio $2-1/(\lceil d/2\rceil+1)$.

Problem

• strategyproof linear regression
• incentive compatibility
• squared-error accuracy
• mechanism design
• approximation ratio

Innovation

• Strategyproof Mechanism
• Linear Regression
• Incentive Compatibility
• Approximation Ratio
• Group Strategyproofness