发表机构
Harvard University（哈佛大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对线性回归中策略证明性与平方误差准确性的权衡，提出确定性群组策略证明机制实现$(d+1)$近似最优，并证明其最优性，同时刻画期望策略证明下的紧比率分离。
AI 中文摘要
我们研究了线性回归中平方误差准确性与激励兼容性之间的权衡。智能体报告与公开已知特征相关联的私有标签，并偏好接近其真实标签的预测。普通最小二乘法（OLS）不一定能诱导真实报告。对于具有 $d$ 个参数的回归，我们设计了一个确定性群组策略证明机制，实现了对最小二乘最优解的 $(d+1)$ 近似，并证明了即使在普遍策略证明的随机化机制中这也是最优的，回答了 Chen 等人（EC 2018）的一个开放问题。将普遍策略证明放宽为期望策略证明揭示了明显的分离：平方个体损失保持因子 $d+1$，而绝对个体损失则达到紧比率 $2-1/(\lceil d/2\rceil+1)$。
英文摘要
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 $2-1/(\lceil d/2\rceil+1)$.
