The goal of strategic classification is to learn decision rules which are robust to strategic input manipulation. Earlier works assume that these responses are known; while some recent works handle unknown responses, they exclusively study online settings with repeated model deployments. But there are many domains$\unicode{x2014}$particularly in public policy, a common motivating use case$\unicode{x2014}$where multiple deployments are infeasible, or where even one bad round is unacceptable. To address this gap, we initiate the formal study of one-shot strategic classification under unknown responses, which requires committing to a single classifier once. Focusing on uncertainty in the users' cost function, we begin by proving that for a broad class of costs, even a small mis-estimation of the true cost can entail trivial accuracy in the worst case. In light of this, we frame the task as a minimax problem, with the goal of identifying the classifier with the smallest worst-case risk over an uncertainty set of possible costs. We design efficient algorithms for both the full-batch and stochastic settings, which we prove converge (offline) to the minimax solution at the dimension-independent rate of $\tilde{\mathcal{O}}(T^{-\frac{1}{2}})$. Our theoretical analysis reveals important structure stemming from strategic responses, particularly the value of dual norm regularization with respect to the cost function.

翻译：摘要：策略分类的目标是学习对策略性输入操纵具有鲁棒性的决策规则。早期研究假设这些反应是已知的；而近期一些工作虽处理未知反应，但仅专注于重复部署模型的在线场景。然而在许多领域——特别是公共政策这一常见激励用例中——多次部署不可行，或甚至一次不良轮次都无法接受。为填补这一空白，我们首次系统研究未知反应下的单次策略分类，要求一次性确定单个分类器。聚焦于用户成本函数的不确定性，我们首先证明：对于广泛一类成本函数，即使对真实成本存在微小误估，在最坏情况下也可能导致平凡精度。基于此，我们将任务建模为极小极大问题，目标是在可能成本的集合中识别具有最小最坏情况风险的分类器。我们设计了适用于全批量和随机设定的高效算法，并证明其以维度无关的速率$\tilde{\mathcal{O}}(T^{-\frac{1}{2}})$（离线）收敛到极小极大解。理论分析揭示了策略反应带来的重要结构，特别是成本函数对偶范数正则化的价值。