Problem
Research questions and friction points this paper is trying to address.
online market making
limit order book
regret minimization
adversarial learning
partial feedback
Optimal Regret for Online Market Making with Limit Order Book
🤖 AI Summary
This study addresses the problem of online market making with limited feedback in limit order books. To overcome the bottleneck of existing high-probability regret bounds, it proposes a learning framework that couples grid discretization with the Hedge algorithm. The core contributions are twofold: first, it breaks the prior $O(T^{2/3})$ barrier by establishing, for the first time, an optimal $O(\sqrt{T})$ high-probability regret bound; second, it rigorously proves the unlearnability of the problem in fully adversarial environments while delineating precise learnability boundaries under stochastic valuation assumptions. Overall, this work provides theoretically complete optimal strategies and a comprehensive characterization for market making scenarios under restricted feedback.
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Online Market Making
Limit Order Book
Regret Bound
Coupled Grids Discretization
Adversarial Learning
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