具有紧保证的凸成本在线选择阈值策略
Threshold Policies with Tight Guarantees for Online Selection with Convex Costs
AI总结：
本文研究带凸成本的在线选择问题，提出一类简单可实现的阈值策略，证明其在确定性算法中的最优性，并表明其竞争比在产量足够大时渐近达到随机算法下界。
摘要：
本文针对带凸成本的在线选择（online selection with convex cost，OSCC）问题，提出了具有紧保证的阈值策略。在OSCC中，卖方希望向一系列买方出售某种资产，以最大化其利润。卖方可以生产额外单位的资产，但边际成本非递减。每个时刻，一名买方到达并给出一个报价。卖方必须立即且不可撤销地决定是否接受该报价，并向该买方生产/出售一单位资产。目标是设计一种在线算法，选择一个买方子集，以最大化卖方利润，即总销售收入减去总生产成本。我们的主要结果是提出了一类简单的阈值策略：它们在逻辑上简单且易于实现，同时在所有确定性算法中具有可证明的最优性保证。我们还推导了随机算法竞争比的下界，并证明当总生产量足够大时，我们的阈值策略的竞争比渐近收敛到该下界。我们的结果推广并统一了多种在线搜索、定价和拍卖问题，并为非递减边际成本对现实世界在线资源分配问题的影响提供了新的视角。
英文摘要：
This paper provides threshold policies with tight guarantees for online selection with convex cost (OSCC). In OSCC, a seller wants to sell some asset to a sequence of buyers with the goal of maximizing her profit. The seller can produce additional units of the asset, but at non-decreasing marginal costs. At each time, a buyer arrives and offers a price. The seller must make an immediate and irrevocable decision in terms of whether to accept the offer and produce/sell one unit of the asset to this buyer. The goal is to develop an online algorithm that selects a subset of buyers to maximize the seller's profit, namely, the total selling revenue minus the total production cost. Our main result is the development of a class of simple threshold policies that are logistically simple and easy to implement, but have provable optimality guarantees among all deterministic algorithms. We also derive a lower bound on competitive ratios of randomized algorithms and prove that the competitive ratio of our threshold policy asymptotically converges to this lower bound when the total production output is sufficiently large. Our results generalize and unify various online search, pricing, and auction problems, and provide a new perspective on the impact of non-decreasing marginal costs on real-world online resource allocation problems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
