AI 中文总结
本研究聚焦在线优化的尾部风险控制，提出纯尾约束刻画期望与最坏情况竞争力的权衡，推导了在线竞价、直线搜索的帕累托最优边界，还构建了自适应TCP确认问题的对应算法并证明非平凡下界。
AI 中文摘要
控制尾部风险是在线优化的重要目标，近期已在竞争分析框架下展开研究。延续这一研究方向，我们探究了纯尾约束，该约束刻画了期望竞争力与最坏情况竞争力之间的权衡关系。针对两个基础搜索问题——在线竞价和直线搜索，我们推导出了这一权衡的帕累托最优边界。\n 随后我们研究了另一个经典问题：TCP确认，其结构与迭代滑雪租赁问题相似。针对该问题，我们构建了一种算法，其权衡特性与滑雪租赁问题已知的帕累托最优权衡一致。该问题的下界推导难度显著更高，因为问题具备自适应结构：在线算法可观测对手的请求（数据包到达），并据此自适应调整自身动作（确认操作）。需要强调的是，此前所有竞争分析语境下的尾部风险研究均局限于非自适应问题，这类问题中算法获得的反馈本质上仅限于表示算法是否成功的二元指示符。尽管如此，我们在该自适应场景中识别出一组由尾界隐含的约束，并证明这些约束可推导出TCP确认问题的一个非平凡下界。
英文摘要
Controlling tail risk is an important objective in online optimization, and recently it has been studied in the context of competitive analysis. Continuing this line of research, we investigate pure tail constraints, which capture the tradeoff between expected and worst-case competitiveness. For two fundamental search problems, online bidding and line search, we derive the Pareto-optimal frontiers of this tradeoff. We then investigate another classic problem, TCP acknowledgment, which has structure similar to the iterated ski rental problem. There, we construct an algorithm whose tradeoff coincides with the known Pareto-optimal tradeoff for ski rental. The lower bounds for this problem are substantially more involved as the problem exhibits adaptive structure: an online algorithm observes requests of the adversary (packet arrivals) and may adaptively adjust its actions (acknowledgments) on this basis. We emphasize that all previous work on tail risk in the context of competitive analysis was restricted to non-adaptive problems, where the feedback given to an algorithm was essentially limited to a binary indicator of whether the algorithm has succeeded or not. Nonetheless, we identify a set of constraints implied by tail bounds in this adaptive setting, and show that they imply a nontrivial lower bound on the TCP acknowledgment problem.
