Market maker algorithms learn better bid ask pricing with less error
Optimal Regret for Online Market Making with Limit Order Book
Computer Science and Game TheoryMachine Learning
Summary
This work studies how a market maker can learn to set good bid and ask prices over time when trading with many buyers and sellers. The authors improve previous methods by designing algorithms that make fewer mistakes, even when the market price changes unpredictably. They also show that if the buyers’ valuation changes completely randomly in a worst-case way, it’s impossible for any algorithm to do well. This helps explain when learning to set prices can and cannot succeed.
What this means in practice
- •For financial technology developers: Create more efficient market making algorithms that adapt quickly to changing prices with guaranteed performance.
- •For algorithmic trading teams: Design pricing strategies that minimize losses from uncertain market conditions using improved online learning techniques.
Authors
Maria Elena Vischi, Francesco Emanuele Stradi, Alberto Marchesi
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.