arXiv:2512.01783cs.LGcs.GT2025-12

提出可应对策略性欺骗的高效主动学习算法,大幅减少标签请求量。

The Active and Noise-Tolerant Strategic Perceptron

  • 设计改进的主动感知机算法,兼顾策略性数据操纵与标签效率。
  • 在单位球面数据下仅需约 O(d ln(1/ε)) 次标签查询即可达 ε 误差。
  • 适用于标签昂贵且存在恶意伪装的场景,如招聘、贷款审核。

我们首次研究了用于分类策略性代理的主动学习算法。主动学习通过选择性标注标签,在标签成本高或耗时的场景(如招聘、录取、贷款决策)中显著提升效率和准确率。然而,策略性分类面临代理人为获取更优结果而篡改特征的问题,导致观测数据失真,带来比干净数据学习更复杂的挑战。目标是设计兼具主动性和抗噪性的算法,在策略环境中仍能准确分类并最小化标签请求。核心难点在于同时应对策略性操纵并保持主动学习的效率优势。我们的主要成果是:在单位球面均匀采样数据下,改进后的主动感知机算法 [DKM05,YZ17] 可在非可实现情况下,以仅 ⌨O(d ln(1/ε)) 次标签查询达到 ε 的额外误差,并最多产生 ⌨O(d ln(1/ε)) 额外误判,即使有 ⌨Ω(ε) 的输入标签与最优分类器不一致。该算法计算高效,所需标签数远低于此前策略感知机工作 [ABBN21]。

原文摘要 · Abstract (English)

We initiate the study of active learning algorithms for classifying strategic agents. Active learning is a well-established framework in machine learning in which the learner selectively queries labels, often achieving substantially higher accuracy and efficiency than classical supervised methods-especially in settings where labeling is costly or time-consuming, such as hiring, admissions, and loan decisions. Strategic classification, however, addresses scenarios where agents modify their features to obtain more favorable outcomes, resulting in observed data that is not truthful. Such manipulation introduces challenges beyond those in learning from clean data. Our goal is to design active and noise-tolerant algorithms that remain effective in strategic environments-algorithms that classify strategic agents accurately while issuing as few label requests as possible. The central difficulty is to simultaneously account for strategic manipulation and preserve the efficiency gains of active learning. Our main result is an algorithm for actively learning linear separators in the strategic setting that preserves the exponential improvement in label complexity over passive learning previously obtained only in the non-strategic case. Specifically, for data drawn uniformly from the unit sphere, we show that a modified version of the Active Perceptron algorithm [DKM05,YZ17] achieves excess error $ε$ using only $\tilde{O}(d \ln \frac{1}ε)$ label queries and incurs at most $\tilde{O}(d \ln \frac{1}ε)$ additional mistakes relative to the optimal classifier, even in the nonrealizable case, when a $\tildeΩ(ε)$ fraction of inputs have inconsistent labels with the optimal classifier. The algorithm is computationally efficient and, under these distributional assumptions, requires substantially fewer label queries than prior work on strategic Perceptron [ABBN21].

主动学习策略性分类感知机

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