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.

翻译：本研究探讨情境信息在交易者间经纪在线学习问题中的作用。在该序列决策问题中，每个时间步会有两位交易者带着对交易资产的秘密估值到达。学习者（经纪人）基于资产与市场条件的情境数据提出交易（或经纪）价格。随后，交易者根据其估值是否高于或低于经纪价格来揭示买入或卖出意愿。当其中一位交易者决定买入而另一位决定卖出时——即经纪人提出的价格介于两者估值的最小值与最大值之间——交易即告成立。我们针对该问题设计了算法，并在多种标准假设下证明了理论遗憾界的最优性保证。