A Parametric Contextual Online Learning Theory of Brokerage

TL;DR

This paper introduces a new online learning framework for brokerage that leverages contextual information to optimize trading prices, providing algorithms with proven regret guarantees.

Contribution

It develops a parametric contextual online learning model for brokerage and offers algorithms with optimal regret bounds under standard assumptions.

Findings

Algorithms achieve optimal regret guarantees

Theoretical analysis confirms effectiveness of the approach

Framework adapts to various market conditions

Abstract

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.