# Trading Volume Maximization with Online Learning

arXiv: https://arxiv.org/abs/2405.13102 · HTML: https://mlsanity.com/paper/2405.13102/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 22 references that are in the map.
- First posted on arXiv 21 May 2024.

## Builds on (most cited first, 13 of 13)

- [Bilateral Trade: A Regret Minimization Perspective](https://mlsanity.com/paper/2109.12974/) (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)
- [Repeated Bilateral Trade Against a Smoothed Adversary](https://mlsanity.com/paper/2302.10805/) (2023)
- [Efficient Two-Sided Markets with Limited Information](https://mlsanity.com/paper/2003.07503/) (2020)
- [Approximating Gains from Trade in Two-sided Markets via Simple Mechanisms](https://mlsanity.com/paper/1706.04637/) (2017)
- [Fixed-Price Approximations in Bilateral Trade](https://mlsanity.com/paper/2107.14327/) (2021)
- [Fixed Price Approximability of the Optimal Gain From Trade](https://mlsanity.com/paper/1710.08394/) (2017)
- [A Nearest Neighbor Characterization of Lebesgue Points in Metric Measure Spaces](https://mlsanity.com/paper/2007.03937/) (2020)
- [An Online Learning Theory of Brokerage](https://mlsanity.com/paper/2310.12107/) (2023)
- [Bulow-Klemperer-Style Results for Welfare Maximization in Two-Sided Markets](https://mlsanity.com/paper/1903.06696/) (2019)
- [Approximately Efficient Two-Sided Combinatorial Auctions](https://mlsanity.com/paper/1611.05342/) (2016)
- [Non-Obvious Manipulability for Single-Parameter Agents and Bilateral Trade](https://mlsanity.com/paper/2202.06660/) (2022)

## Abstract (arXiv)

We explore brokerage between traders in an online learning framework. At any round t, two traders meet to exchange an asset, provided the exchange is mutually beneficial. The broker proposes a trading price, and each trader tries to sell their asset or buy the asset from the other party, depending on whether the price is higher or lower than their private valuations. A trade happens if one trader is willing to sell and the other is willing to buy at the proposed price. Previous work provided guidance to a broker aiming at enhancing traders' total earnings by maximizing the gain from trade, defined as the sum of the traders' net utilities after each interaction. In contrast, we investigate how the broker should behave to maximize the trading volume, i.e., the total number of trades. We model the traders' valuations as an i.i.d. process with an unknown distribution. If the traders' valuations are revealed after each interaction (full-feedback), and the traders' valuations cumulative distribution function (cdf) is continuous, we provide an algorithm achieving logarithmic regret and show its optimality up to constant factors. If only their willingness to sell or buy at the proposed price is revealed after each interaction (2-bit feedback), we provide an algorithm achieving poly-logarithmic regret when the traders' valuations cdf is Lipschitz and show that this rate is near-optimal. We complement our results by analyzing the implications of dropping the regularity assumptions on the unknown traders' valuations cdf. If we drop the continuous cdf assumption, the regret rate degrades to Theta(√T) in the full-feedback case, where T is the time horizon. If we drop the Lipschitz cdf assumption, learning becomes impossible in the 2-bit feedback case.