# A Parametric Contextual Online Learning Theory of Brokerage

arXiv: https://arxiv.org/abs/2407.01566 · HTML: https://mlsanity.com/paper/2407.01566/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 65 references that are in the map.
- First posted on arXiv 22 May 2024.

## Builds on (most cited first, 30 of 37)

- [Instance-Dependent Complexity of Contextual Bandits and Reinforcement Learning: A Disagreement-Based Perspective](https://mlsanity.com/paper/2010.03104/) (2020)
- [Efficient Contextual Bandits in Non-stationary Worlds](https://mlsanity.com/paper/1708.01799/) (2017)
- [Model selection for contextual bandits](https://mlsanity.com/paper/1906.00531/) (2019)
- [Dynamic Pricing in High-dimensions](https://mlsanity.com/paper/1609.07574/) (2016)
- [Efficient and Robust Algorithms for Adversarial Linear Contextual Bandits](https://mlsanity.com/paper/2002.00287/) (2020)
- [Contextual Bandits with Continuous Actions: Smoothing, Zooming, and Adapting](https://mlsanity.com/paper/1902.01520/) (2019)
- [Learning Prices for Repeated Auctions with Strategic Buyers](https://mlsanity.com/paper/1311.6838/) (2013)
- [Dynamic Incentive-aware Learning: Robust Pricing in Contextual Auctions](https://mlsanity.com/paper/2002.11137/) (2020)
- [Contextual Bandits with Packing and Covering Constraints: A Modular Lagrangian Approach via Regression](https://mlsanity.com/paper/2211.07484/) (2022)
- [Bilateral Trade: A Regret Minimization Perspective](https://mlsanity.com/paper/2109.12974/) (2021)
- [Multidimensional Binary Search for Contextual Decision-Making](https://mlsanity.com/paper/1611.00829/) (2016)
- [Contextual Search via Intrinsic Volumes](https://mlsanity.com/paper/1804.03195/) (2018)
- [Smooth Contextual Bandits: Bridging the Parametric and Non-differentiable Regret Regimes](https://mlsanity.com/paper/1909.02553/) (2019)
- [Policy Optimization Using Semi-parametric Models for Dynamic Pricing](https://mlsanity.com/paper/2109.06368/) (2021)
- [Logarithmic Regret in Feature-based Dynamic Pricing](https://mlsanity.com/paper/2102.10221/) (2021)
- [Distribution-free Contextual Dynamic Pricing](https://mlsanity.com/paper/2109.07340/) (2021)
- [Taking a hint: How to leverage loss predictors in contextual bandits?](https://mlsanity.com/paper/2003.01922/) (2020)
- [A Regret Analysis of Bilateral Trade](https://mlsanity.com/paper/2102.08754/) (2021)
- [Learning to Bid in Contextual First Price Auctions](https://mlsanity.com/paper/2109.03173/) (2021)
- [Contexts can be Cheap: Solving Stochastic Contextual Bandits with Linear Bandit Algorithms](https://mlsanity.com/paper/2211.05632/) (2022)
- [Stochastic Bandits with Context Distributions](https://mlsanity.com/paper/1906.02685/) (2019)
- [Semi-parametric dynamic contextual pricing](https://mlsanity.com/paper/1901.02045/) (2019)
- [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)
- [The Role of Transparency in Repeated First-Price Auctions with Unknown Valuations](https://mlsanity.com/paper/2307.09478/) (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)
- [Contextual bandits with surrogate losses: Margin bounds and efficient algorithms](https://mlsanity.com/paper/1806.10745/) (2018)
- [Fixed-Price Approximations in Bilateral Trade](https://mlsanity.com/paper/2107.14327/) (2021)
- [Approximately Efficient Bilateral Trade](https://mlsanity.com/paper/2111.03611/) (2021)

## Built on by (most cited first, 4 of 4)

- [Market Making without Regret](https://mlsanity.com/paper/2411.13993/) (2024)
- [A Tight Regret Analysis of Non-Parametric Repeated Contextual Brokerage](https://mlsanity.com/paper/2503.02646/) (2025)
- [Bilateral Trade Under Heavy-Tailed Valuations: Minimax Regret without a Variance Bound](https://mlsanity.com/paper/2603.06851/) (2026)
- [Profit Maximization in Bilateral Trade against a Smooth Adversary](https://mlsanity.com/paper/2605.12664/) (2026)

## Abstract (arXiv)

We study the role of contextual information in the online learning problem of brokerage between traders. In this sequential problem, at each time step, two traders arrive with secret valuations about an asset they wish to trade. The learner (a broker) suggests a trading (or brokerage) price based on contextual data about the asset and the market conditions. Then, the traders reveal their willingness to buy or sell based on whether their valuations are higher or lower than the brokerage price. A trade occurs if one of the two traders decides to buy and the other to sell, i.e., if the broker's proposed price falls between the smallest and the largest of their two valuations. We design algorithms for this problem and prove optimal theoretical regret guarantees under various standard assumptions.