发表机构
Adam Mickiewicz University; Poznań University of Economics and Business（亚当·密茨凯维奇大学; 波兹南经济与商业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究生长树中的在线最大基数匹配，针对增长规律未知或错误指定的情况，提出阈值策略并证明其鲁棒性，同时给出参数估计方法，实现亚线性遗憾。
AI 中文摘要
我们研究在连续叶附着揭示的树中，具有已知时间范围和被错误指定或未知的外生增长规律的不可撤销的最大基数匹配。对于具有非负度强化的确定性仿射附着预测，最优阈值策略相对于知道实际增长规律的在线预言机，其损失至多为累积期望条件全变差误差的两倍。这源于贝尔曼续值函数的单位跨度性质，且没有额外的时间范围因子。一个四顶点示例达到了指定确定性策略的系数二，而一个双模型论证给出了在一般错误指定下任意策略的模型误差预算的线性下界。对于均匀偏好附着，局部误差通过叶计数具有精确表达式。当其常数混合参数未知时，我们从同一生长树中估计它，并在几何时间更新阈值策略。个体贝尔曼价格的参数敏感性界和均匀度矩估计产生期望遗憾 $O(\sqrt{n}\log^2 n)$，使用 $O(n^2\log n)$ 次算术运算和 $O(n)$ 个存储条目。精确的极小极大速率仍然开放。
英文摘要
We study irrevocable maximum-cardinality matching in trees revealed by successive leaf attachments, with a known horizon and an exogenous growth law that is misspecified or unknown. For deterministic affine attachment forecasts with nonnegative degree reinforcement, the optimal threshold policy loses at most twice the cumulative expected conditional total-variation error relative to an online oracle knowing the actual growth law. This follows from a unit-span property of the Bellman continuation score and has no additional horizon factor. A four-vertex example attains the coefficient two for the specified deterministic policy, and a two-model argument gives a lower bound linear in the model-error budget for arbitrary policies under general misspecification. For uniform-preferential attachment, the local error has an exact expression through the leaf count. When its constant mixture parameter is unknown, we estimate it from the same growing tree and update the threshold policy at geometric times. A parameter-sensitivity bound for individual Bellman prices and uniform degree-moment estimates yield expected regret $O(\sqrt{n}\log^2 n)$, using $O(n^2\log n)$ arithmetic operations and $O(n)$ stored entries. The exact minimax rate remains open.
Comments14 pages, 1 figure, 1 table
