Online Market Making and the Value of Observing the Order Book

Davide Maran, Marcello Restelli
Proceedings of Thirty Ninth Conference on Learning Theory, PMLR 336:4969-4998, 2026.

Abstract

We study an online market-making problem in which a learner sequentially posts bid and ask prices for a single asset while interacting with traders holding private valuations. Unlike existing online learning formulations that assume fully censored feedback, we introduce an action-dependent feedback model inspired by real limit order books: when a trade occurs, the trader’s valuation remains hidden, whereas when no trade occurs, informative feedback about supply and demand is revealed. We show that this additional information fundamentally changes the learnability of the problem. In the stochastic setting with i.i.d. market prices, we propose an elimination-based algorithm that achieves $\widetilde O(\sqrt{T})$ regret with high probability, without requiring any smoothness assumptions on the distribution of trader valuations. We then extend this result to a broad class of mean-reverting price processes by considering both local, autoregressive dynamics and a weaker global drift condition based on cumulative deviations from the mean. Under either assumption, we establish high-probability $\widetilde O(\sqrt{T})$ regret bounds, relying on a new concentration inequality of independent interest. Finally, in the adversarial setting with oblivious prices, we design an explore-then-perturb algorithm that guarantees $\tilde O(T^{2/3})$ regret in expectation. Our results quantify the value of observing the order book in online market making and demonstrate that even limited, action-dependent feedback can substantially improve regret guarantees compared to standard bandit feedback models.

Cite this Paper

BibTeX
@InProceedings{pmlr-v336-maran26a, title = {Online Market Making and the Value of Observing the Order Book}, author = {Maran, Davide and Restelli, Marcello}, booktitle = {Proceedings of Thirty Ninth Conference on Learning Theory}, pages = {4969--4998}, year = {2026}, editor = {Hanneke, Steve and Lattimore, Tor}, volume = {336}, series = {Proceedings of Machine Learning Research}, month = {29 Jun--03 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v336/main/assets/maran26a/maran26a.pdf}, url = {https://proceedings.mlr.press/v336/maran26a.html}, abstract = {We study an online market-making problem in which a learner sequentially posts bid and ask prices for a single asset while interacting with traders holding private valuations. Unlike existing online learning formulations that assume fully censored feedback, we introduce an action-dependent feedback model inspired by real limit order books: when a trade occurs, the trader’s valuation remains hidden, whereas when no trade occurs, informative feedback about supply and demand is revealed. We show that this additional information fundamentally changes the learnability of the problem. In the stochastic setting with i.i.d. market prices, we propose an elimination-based algorithm that achieves $\widetilde O(\sqrt{T})$ regret with high probability, without requiring any smoothness assumptions on the distribution of trader valuations. We then extend this result to a broad class of mean-reverting price processes by considering both local, autoregressive dynamics and a weaker global drift condition based on cumulative deviations from the mean. Under either assumption, we establish high-probability $\widetilde O(\sqrt{T})$ regret bounds, relying on a new concentration inequality of independent interest. Finally, in the adversarial setting with oblivious prices, we design an explore-then-perturb algorithm that guarantees $\tilde O(T^{2/3})$ regret in expectation. Our results quantify the value of observing the order book in online market making and demonstrate that even limited, action-dependent feedback can substantially improve regret guarantees compared to standard bandit feedback models.} }
Endnote
%0 Conference Paper %T Online Market Making and the Value of Observing the Order Book %A Davide Maran %A Marcello Restelli %B Proceedings of Thirty Ninth Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2026 %E Steve Hanneke %E Tor Lattimore %F pmlr-v336-maran26a %I PMLR %P 4969--4998 %U https://proceedings.mlr.press/v336/maran26a.html %V 336 %X We study an online market-making problem in which a learner sequentially posts bid and ask prices for a single asset while interacting with traders holding private valuations. Unlike existing online learning formulations that assume fully censored feedback, we introduce an action-dependent feedback model inspired by real limit order books: when a trade occurs, the trader’s valuation remains hidden, whereas when no trade occurs, informative feedback about supply and demand is revealed. We show that this additional information fundamentally changes the learnability of the problem. In the stochastic setting with i.i.d. market prices, we propose an elimination-based algorithm that achieves $\widetilde O(\sqrt{T})$ regret with high probability, without requiring any smoothness assumptions on the distribution of trader valuations. We then extend this result to a broad class of mean-reverting price processes by considering both local, autoregressive dynamics and a weaker global drift condition based on cumulative deviations from the mean. Under either assumption, we establish high-probability $\widetilde O(\sqrt{T})$ regret bounds, relying on a new concentration inequality of independent interest. Finally, in the adversarial setting with oblivious prices, we design an explore-then-perturb algorithm that guarantees $\tilde O(T^{2/3})$ regret in expectation. Our results quantify the value of observing the order book in online market making and demonstrate that even limited, action-dependent feedback can substantially improve regret guarantees compared to standard bandit feedback models.
APA
Maran, D. & Restelli, M.. (2026). Online Market Making and the Value of Observing the Order Book. Proceedings of Thirty Ninth Conference on Learning Theory, in Proceedings of Machine Learning Research 336:4969-4998 Available from https://proceedings.mlr.press/v336/maran26a.html.

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