# Market Making without Regret

arXiv: https://arxiv.org/abs/2411.13993 · HTML: https://mlsanity.com/paper/2411.13993/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 75 references that are in the map.
- First posted on arXiv 21 Nov 2024.

## Builds on (most cited first, 25 of 25)

- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [Introduction to Multi-Armed Bandits](https://mlsanity.com/paper/1904.07272/) (2019)
- [Online Learning: A Modern Introduction Using Convex Optimization](https://mlsanity.com/paper/1912.13213/) (2019)
- [Bandits with Knapsacks](https://mlsanity.com/paper/1305.2545/) (2013)
- [Smoothed Analysis with Adaptive Adversaries](https://mlsanity.com/paper/2102.08446/) (2021)
- [Smoothed Online Learning is as Easy as Statistical Learning](https://mlsanity.com/paper/2202.04690/) (2022)
- [Smoothed Analysis of Online and Differentially Private Learning](https://mlsanity.com/paper/2006.10129/) (2020)
- [Online learning in repeated auctions](https://mlsanity.com/paper/1511.05720/) (2015)
- [Optimal No-regret Learning in Repeated First-price Auctions](https://mlsanity.com/paper/2003.09795/) (2020)
- [Bilateral Trade: A Regret Minimization Perspective](https://mlsanity.com/paper/2109.12974/) (2021)
- [Dynamic Pricing with Finitely Many Unknown Valuations](https://mlsanity.com/paper/1807.03288/) (2018)
- [Distribution-free Contextual Dynamic Pricing](https://mlsanity.com/paper/2109.07340/) (2021)
- [A Regret Analysis of Bilateral Trade](https://mlsanity.com/paper/2102.08754/) (2021)
- [No-Regret Learning in Bilateral Trade via Global Budget Balance](https://mlsanity.com/paper/2310.12370/) (2023)
- [An α-regret analysis of Adversarial Bilateral Trade](https://mlsanity.com/paper/2210.06846/) (2022)
- [Pushing the Efficiency-Regret Pareto Frontier for Online Learning of Portfolios and Quantum States](https://mlsanity.com/paper/2202.02765/) (2022)
- [Repeated Bilateral Trade Against a Smoothed Adversary](https://mlsanity.com/paper/2302.10805/) (2023)
- [The Role of Transparency in Repeated First-Price Auctions with Unknown Valuations](https://mlsanity.com/paper/2307.09478/) (2023)
- [An Online Learning Theory of Brokerage](https://mlsanity.com/paper/2310.12107/) (2023)
- [Fast Rate Learning in Stochastic First Price Bidding](https://mlsanity.com/paper/2107.01835/) (2021)
- [Learning to Price Against a Moving Target](https://mlsanity.com/paper/2106.04689/) (2021)
- [Feature-Based Online Bilateral Trade](https://mlsanity.com/paper/2405.18183/) (2024)
- [Fair Online Bilateral Trade](https://mlsanity.com/paper/2405.13919/) (2024)
- [A Parametric Contextual Online Learning Theory of Brokerage](https://mlsanity.com/paper/2407.01566/) (2024)
- [Adaptive maximization of social welfare](https://mlsanity.com/paper/2310.09597/) (2023)

## Built on by (most cited first, 5 of 5)

- [Learning Market Making with Closing Auctions](https://mlsanity.com/paper/2601.17247/) (2026)
- [Profit Maximization in Bilateral Trade against a Smooth Adversary](https://mlsanity.com/paper/2605.12664/) (2026)
- [The Invisible Handshake: Persistent Overpricing by Adaptive Market Agents](https://mlsanity.com/paper/2510.15995/) (2025)
- [Online Market Making and the Value of Observing the Order Book](https://mlsanity.com/paper/2605.19584/) (2026)
- [Optimal Regret for Online Market Making with Limit Order Book](https://mlsanity.com/paper/2610.09691/) (2026)

## Abstract (arXiv)

We consider a sequential decision-making setting where, at every round t, a market maker posts a bid price Bt and an ask price At to an incoming trader (the taker) with a private valuation for one unit of some asset. If the trader's valuation is lower than the bid price, or higher than the ask price, then a trade (sell or buy) occurs. If a trade happens at round t, then letting Mt be the market price (observed only at the end of round t), the maker's utility is Mt - Bt if the maker bought the asset, and At - Mt if they sold it. We characterize the maker's regret with respect to the best fixed choice of bid and ask pairs under a variety of assumptions (adversarial, i.i.d., and their variants) on the sequence of market prices and valuations. Our upper bound analysis unveils an intriguing connection relating market making to first-price auctions and dynamic pricing. Our main technical contribution is a lower bound for the i.i.d. case with Lipschitz distributions and independence between prices and valuations. The difficulty in the analysis stems from the unique structure of the reward and feedback functions, allowing an algorithm to acquire information by graduating the "cost of exploration" in an arbitrary way.