arXiv：cs.LG· Maria Elena Vischi, Francesco Emanuele Stradi, Alberto Marchesi·· 4 小时前AI 评分36
限价订单簿下在线做市的最优遗憾界
Optimal Regret for Online Market Making with Limit Order Book
AI 导读
针对限价订单簿反馈模型下的在线做市问题，研究者将原有期望遗憾界从 Õ(T^{2/3}) 改进为高概率 Õ(√T)。方法基于两个耦合网格对买卖价空间做离散化并结合 Hedge 算法，在交易员估值 i.i.d.、市场价格对抗选择的假设下，将该保证扩展到限价订单簿诱导的弱反馈场景。研究还证明，当市场价格与交易员估值均为对抗性时，即使全反馈也无法实现次线性遗憾。
正文
Abstract:We study online learning in market making, where, at each round, a market maker posts bid and ask prices before observing the market price and the private valuation of an incoming trader. In this setting, Maran et al. 2026 introduce a feedback model motivated by limit order books, in which the trader's valuation is revealed only if no transaction occurs. Assuming that trader valuations are drawn i.i.d. from an unknown distribution while market prices are chosen adversarially, they establish an expected regret bound of $\widetilde{\mathcal{O}}(T^{2/3})$. In this work, we improve upon this guarantee by establishing a high-probability regret bound of $\widetilde{\mathcal{O}}(\sqrt{T})$. As a warm-up, we first consider the full-feedback setting. We introduce a discretization of the bid-ask space based on two coupled grids and combine it with Hedge to achieve the desired regret rate. Building on these ideas, we then address the substantially weaker feedback induced by a limit order book and develop an algorithm that achieves the same guarantee. Finally, we investigate the limits of learnability in fully adversarial environments, where the valuations may vary arbitrarily as well. Perhaps surprisingly, we show that when both market prices and trader valuations are chosen adversarially, sublinear regret is impossible even under full feedback, thereby motivating our stochastic assumption on the valuations.
| Subjects: | Computer Science and Game Theory (cs.GT); Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.09691 [cs.GT] |
| (or arXiv:2610.09691v1 [cs.GT] for this version) | |
| https://doi.org/10.48550/arXiv.2610.09691 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Maria Elena Vischi [view email]
[v1]
Wed, 7 Oct 2026 08:51:54 UTC (40 KB)
来源：arXiv：cs.LG · arxiv.org