A primary goal in strategic classification is to learn decision rules which are robust to strategic input manipulation. Earlier works assume that strategic responses are known; while some recent works address the important challenge of unknown responses, they exclusively study sequential settings which allow multiple model deployments over time. But there are many domains$\unicode{x2014}$particularly in public policy, a common motivating use-case$\unicode{x2014}$where multiple deployments are unrealistic, or where even a single bad round is undesirable. To address this gap, we initiate the study of strategic classification under unknown responses in the one-shot setting, which requires committing to a single classifier once. Focusing on the users' cost function as the source of uncertainty, we begin by proving that for a broad class of costs, even a small mis-estimation of the true cost can entail arbitrarily low accuracy in the worst case. In light of this, we frame the one-shot 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. Our main contribution is efficient algorithms for both the full-batch and stochastic settings, which we prove converge (offline) to the minimax optimal solution at the dimension-independent rate of $\tilde{\mathcal{O}}(T^{-\frac{1}{2}})$. Our analysis reveals important structure stemming from the strategic nature of user responses, particularly the importance of dual norm regularization with respect to the cost function.

翻译：策略分类的核心目标之一是学习对策略性输入操纵具有鲁棒性的决策规则。早期研究假设策略性响应已知；而近期部分工作虽致力于应对未知响应的重大挑战，但仅局限于可随时间多次部署模型的序列化设定。然而在许多领域——特别是作为常见应用案例的公共政策中，多次部署不切实际，即便单次不良轮次也难以接受。为填补这一空白，我们首次将未知响应下的策略分类研究拓展至单次博弈设定，该设定要求一次性确定分类器。以用户成本函数作为不确定性来源，我们首先证明：对于广泛类别成本函数，即使真实成本存在微小误估，在最坏情况下也可能导致任意低的准确率。鉴于此，我们将单次博弈任务建模为极小极大问题，目标是在可能成本的未知集上寻找具有最小最坏情况风险的最优分类器。我们的主要贡献是为全批量和随机两种场景设计了高效算法，并证明其能（离线）收敛至极小极大最优解，收敛速率达到与维度无关的 $\tilde{\mathcal{O}}(T^{-\frac{1}{2}})$。理论分析揭示了由用户策略性响应产生的关键结构，特别是基于成本函数的对偶范数正则化的重要性。