带尾部约束的随机在线竞价的原始-对偶方法
A Primal-Dual Approach to Randomized Online Bidding with Tail Constraints
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中文总结 AI 辅助
本文提出原始-对偶方法，研究带尾部约束的随机在线竞价问题，确定纯尾部约束下的最优期望竞争比，并给出一般尾部约束的参数相关上界。
中文摘要 AI 辅助
控制随机算法中的尾部风险已受到越来越多的关注。最近提出的一种方法是对尾部施加约束，以限制出现不良结果的概率。我们在此类尾部约束下研究随机在线竞价问题。当尾部约束要求超过规定阈值的概率为零时，我们确定了最优期望竞争比。对于允许正超额概率的一般尾部约束，我们推导出最优期望竞争比的一个参数相关上界。这项工作基于Royce Kraakman的硕士论文，该论文启动了我们关于在线竞价尾部约束的研究。本文中确立的最优性结果，特别是纯尾部约束的匹配下界，是后来获得的，并未包含在该论文中。在了解到Basiak等人关于纯尾部约束的独立相关工作后，我们决定在稿件仍在开发期间公开此初步版本。论文中的部分材料尚未纳入当前版本。
英文摘要
Controlling tail risk in randomized algorithms has received increasing attention. A recently introduced approach is to impose tail constraints that limit the probability of poor outcomes. We study the randomized online bidding problem under such tail constraints. When the tail constraints require zero probability of exceeding the prescribed thresholds, we determine the optimal expected competitive ratio. For general tail constraints that allow positive exceedance probabilities, we derive a parameter-dependent upper bound on the optimal expected competitive ratio. This work builds on the Master's thesis of Royce Kraakman, which initiated our study of tail constraints for online bidding. The optimality result established in the present paper, in particular the matching lower bound for pure tail constraints, was obtained subsequently and is not contained in the thesis. After becoming aware of independent related work by Basiak et al. on pure tail constraints, we decided to make this preliminary version publicly available while the manuscript is still under development. Some material from the thesis has not yet been incorporated into the present version.
