发表机构
Yale University; University of Toronto; Carnegie Mellon University（耶鲁大学; 多伦多大学; 卡内基梅隆大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出STARS算法，用于带存储约束的在线交易，通过模拟未来价格场景近似值函数，在广泛分布下达到接近最优的遗憾性能，并揭示中位数间隙与初始库存为零导致的基本极限谱。
AI 中文摘要
我们研究了一个在线交易问题，其中交易者面对从已知分布$F$（定义在$[0,1]$上）中独立同分布抽取的价格序列，必须在存储约束下做出不可撤销的买入、卖出或持有决策。我们以遗憾（即事后最优策略（已知整个价格序列）的期望利润与在线算法期望利润之差）来衡量可实现的算法性能。我们分析了有限原子分布和连续分布，这些分布通过其在中位数附近的行为来刻画，我们使用参数$\beta$来量化价格质量围绕分布中位数的聚集程度。我们识别出算法性能的一个新驱动因素，证明中位数间隙与初始库存水平为零相结合，可以迫使遗憾缩放为$\Omega(T^{(\beta+1)/(2\beta+4)})$——这建立了算法性能基本极限的一个新谱系。然后我们研究了STARS（即跨多个场景重复平均的存储交易），它模拟可能的未来价格场景以近似值函数并进行买入/卖出/持有决策。我们证明STARS在广泛分布范围内获得接近最优的算法性能（达到多对数因子）。特别是，对于有限原子价格，它实现$O(\log T)$遗憾；对于无中位数间隙的连续分布，实现$\widetilde{O}(T^{\beta/(2\beta+2)})$遗憾；对于有中位数间隙的连续分布且$\beta \geq 0$，实现$\widetilde{O}(T^{(\beta+1)/(2\beta+4)})$遗憾。
英文摘要
We study an online trading problem where a trader, given a sequence of i.i.d. prices drawn from a known distribution $F$ on $[0,1]$, must make irrevocable buy, sell, or hold decisions subject to storage constraints. We investigate achievable algorithmic performance measured in terms of regret, the difference between the expected profit of the hindsight optimal policy that knows the entire price sequence and an online algorithm. We analyze finite atomic and continuous distributions characterized by their local behavior around the median which we capture using a parameter $β$. The parameter $β$ quantifies how the mass of prices accumulates around the distribution median. We identify a new driver of algorithmic performance, demonstrating that median gaps coupled with an initial inventory level of zero can force regret scaling of $Ω(T^{(β+ 1)/(2β+4)})$ --- establishing a novel spectrum of fundamental limits on algorithmic performance. We then study STARS, short for Storage Trading by Averaging Repeatedly across multiple Scenarios, which simulates possible future price scenarios to approximate the value-to-go function and make buy/sell/hold decisions. We show that STARS obtain near-optimal algorithmic performance (upto poly-logarithmic factors) across a broad range of distributions. In particular, it achieves $O(\log T)$ regret for finite atomic prices, $\widetilde{O}(T^{β/(2β+2)})$ for continuous distributions without a median gap and $\widetilde{O}(T^{(β+1)/(2β+4)})$ for continuous distributions with a median gap for $β\geq 0$.
