库存约束下的竞争在线优化
Competitive Online Optimization under Inventory Constraints
AI总结：
本文研究库存约束下的在线优化问题，提出新算法框架CR-Pursuit，在确定性算法中实现最小竞争比，并统一推广了单向交易等问题的竞争比界限。
摘要：
本文研究库存（预算）约束下的在线优化问题。虽然在线优化是一个被广泛研究的课题，但带有库存约束的版本已被证明十分困难。我们考虑了一种库存约束优化的公式化表述，它是经典单向交易问题的推广，并具有广泛的应用范围。我们提出了一个新的算法框架CR-Pursuit，并证明它在库存约束在线优化中，在所有确定性算法里实现了最小的竞争比（至多相差一个与问题相关的常数因子）。我们的算法及其分析不仅简化和统一了标准单向交易问题的最先进结果，还为包括凹收益函数在内的推广确立了新的界限。例如，对于具有价格弹性的单向交易，CR-Pursuit算法实现的竞争比与下界$\ln θ+1$仅相差一个小的加性常数（即1/3），其中$θ$是最大和最小基础价格之间的比率。
英文摘要：
This paper studies online optimization under inventory (budget) constraints. While online optimization is a well-studied topic, versions with inventory constraints have proven difficult. We consider a formulation of inventory-constrained optimization that is a generalization of the classic one-way trading problem and has a wide range of applications. We present a new algorithmic framework, \textsf{CR-Pursuit}, and prove that it achieves the minimal competitive ratio among all deterministic algorithms (up to a problem-dependent constant factor) for inventory-constrained online optimization. Our algorithm and its analysis not only simplify and unify the state-of-the-art results for the standard one-way trading problem, but they also establish novel bounds for generalizations including concave revenue functions. For example, for one-way trading with price elasticity, the \textsf{CR-Pursuit} algorithm achieves a competitive ratio that is within a small additive constant (i.e., 1/3) to the lower bound of $\ln θ+1$, where $θ$ is the ratio between the maximum and minimum base prices.
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。
