具有有界适应性的风险敏感在线选择
Risk-Sensitive Online Selection with Bounded Adaptivity
AI总结：
本文研究在线对抗选择中风险敏感与有界适应性的平衡，提出一种相关定价机制以提升尾部性能，同时在静态和动态定价下提供竞争保障。
摘要：
设计在期望和不利随机实现下均能可靠运行的随机在线算法是在线决策中的基本挑战。本文研究在线对抗选择中的这一挑战，其中决策者通过定价向依次到来的买家分配资源。我们关注两个常被忽视的方面：尾部风险敏感性和有界适应性，其中尾部风险通过条件价值-at-风险（CVaR）测量，有界适应性限制了允许的策略更新次数。我们的主要贡献是一种相关定价机制，使用单一随机种子协调时间内的定价决策。这种相关性在样本路径上诱导定价配置的单调排序，从而提升下尾性能同时尊重适应性约束。更广泛地说，我们的结果突显相关性作为控制随机在线算法尾部风险的机制。使用此框架，我们为问题的不同 regime 在静态和动态定价下推导了竞争保障。我们的分析发展了一种针对CVaR目标的随机在线对偶框架，并揭示了允许的适应性、风险敏感性和竞争性能之间的系统性权衡。在真实航空定价数据上的实验进一步展示了相关定价对福利集中和尾部行为的实证影响。
英文摘要：
Designing randomized online algorithms that perform reliably not only in expectation but also under unfavorable realizations of randomness is a fundamental challenge in online decision-making. In this paper, we study this challenge in online adversarial selection, where a decision maker allocates $k$ units of a resource to sequentially arriving buyers through posted prices. We focus on two intertwined considerations that are often overlooked simultaneously: tail-risk sensitivity and bounded adaptivity, where tail risk is measured using conditional value-at-risk (CVaR) and bounded adaptivity limits the number of allowable policy updates over time. Our main contribution is a correlated posted-price mechanism that uses a single random seed to coordinate pricing decisions across time. This correlation induces a monotonic ordering of pricing profiles across sample paths, improving lower-tail performance while respecting the adaptivity constraint. More broadly, our results highlight correlation as a mechanism for controlling tail risk in randomized online algorithms. Using this framework, we derive competitive guarantees for several regimes of the problem under both static and dynamic pricing. Our analysis develops a risk-sensitive randomized online primal-dual framework tailored to CVaR objectives and reveals a systematic trade-off between allowable adaptivity, risk sensitivity, and competitive performance. Experiments on real airline pricing data further illustrate the empirical impact of correlated pricing on welfare concentration and tail behavior.
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