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.

We study the following sequential machine learning problem. During each of a sequence of interactions, the learner (a broker) suggests a trading (or brokerage) price to two traders 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 performance guarantees under various standard assumptions.