策略噪声在线性回归中的作用
The Effect of Strategic Noise in Linear Regression
摘要：
我们建立在一个新兴的工作线，研究提供给机器学习算法的训练数据中的策略操作。具体来说，我们专注于无处不在的线性回归任务。以前的工作集中在防策略算法的设计上，其目的是通过调整数据源的激励来完全防止这种操纵。然而，在实践中使用的算法往往不是防策略的，这会导致代理之间的策略博弈。我们专注于一个广泛的非strategypproof算法的线性回归，即$\ell_p$范数最小化（$p > 1$）与凸正则化。我们表明，当操纵有界，在这个类中的每一个算法承认一个唯一的纯纳什均衡的结果。我们还揭示了这种均衡的结构，揭示了一个令人惊讶的连接之间的strategyproof算法和纯纳什均衡的非strategyproof算法在更广泛的设置，这可能是独立的利益。最后，我们从无政府状态的无政府代价的角度分析了这些算法下均衡的质量。
英文摘要：
We build on an emerging line of work which studies strategic manipulations in training data provided to machine learning algorithms. Specifically, we focus on the ubiquitous task of linear regression. Prior work focused on the design of strategyproof algorithms, which aim to prevent such manipulations altogether by aligning the incentives of data sources. However, algorithms used in practice are often not strategyproof, which induces a strategic game among the agents. We focus on a broad class of non-strategyproof algorithms for linear regression, namely $\ell_p$ norm minimization ($p > 1$) with convex regularization. We show that when manipulations are bounded, every algorithm in this class admits a unique pure Nash equilibrium outcome. We also shed light on the structure of this equilibrium by uncovering a surprising connection between strategyproof algorithms and pure Nash equilibria of non-strategyproof algorithms in a broader setting, which may be of independent interest. Finally, we analyze the quality of equilibria under these algorithms in terms of the price of anarchy.
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