We consider an online strategic classification problem where each arriving agent can manipulate their true feature vector to obtain a positive predicted label, while incurring a cost that depends on the amount of manipulation. The learner seeks to predict the agent's true label given access to only the manipulated features. After the learner releases their prediction, the agent's true label is revealed. Previous algorithms such as the strategic perceptron guarantee finitely many mistakes under a margin assumption on agents' true feature vectors. However, these are not guaranteed to encourage agents to be truthful. Promoting truthfulness is intimately linked to obtaining adequate margin on the predictions, thus we provide two new algorithms aimed at recovering the maximum margin classifier in the presence of strategic agent behavior. We prove convergence, finite mistake and finite manipulation guarantees for a variety of agent cost structures. We also provide generalized versions of the strategic perceptron with mistake guarantees for different costs. Our numerical study on real and synthetic data demonstrates that the new algorithms outperform previous ones in terms of margin, number of manipulation and number of mistakes.

翻译：我们考虑一个在线策略分类问题，其中每个到达的智能体可以操纵其真实特征向量以获得正预测标签，同时承担取决于操纵量的成本。学习者只能通过被操纵的特征来预测智能体的真实标签，并在学习者发布预测后揭示智能体的真实标签。以往的算法（如策略感知机）在智能体真实特征向量满足间隔假设时能保证有限次错误，但这些算法无法确保促进智能体的诚实性。促进诚实性与在预测上获得足够间隔密切相关，因此我们提出两种新算法，旨在存在策略性智能体行为时恢复最大间隔分类器。我们证明了在多种智能体成本结构下的收敛性、有限错误和有限操纵保证。我们还为不同成本结构提供了具有错误保证的广义策略感知机版本。在真实数据和合成数据上的数值研究表明，新算法在间隔、操纵次数和错误次数方面均优于以往算法。