broker在不确定市场中通过上下文优化定价，实现近最优交易收益。
A Tight Regret Analysis of Non-Parametric Repeated Contextual Brokerage
- 基于上下文信息动态调整报价，利用相似上下文预测市场价。
- 在全反馈与有限反馈下均达到紧致的后悔界，表现接近理想情况。
- 证明了理想策略至少能实现完全知情策略一半的交易收益，适合在线决策研究者。
我们研究了一种上下文化的重复经纪问题。每次交互中，两名拥有私有价值评估的交易者根据经纪人提出的、受上下文信息影响的价格决定买卖。经纪人的目标是最大化交易者的净效用（即交易收益），通过最小化相对于已知交易者价值分布的代理（oracle）的后悔值来实现。我们假设交易者的价值是未知物品当前市场价格的零均值扰动，且该价格可任意变化；同时，相似的上下文应对应相似的市场价格。我们分析了两种反馈机制：全反馈（每次交互后披露交易者的真实价值）和有限反馈（仅披露交易尝试结果）。针对两种反馈，我们提出了实现紧致后悔界的算法。此外，我们进一步证明了一个紧致的1/2-近似结果：已知价值分布的代理所能实现的交易收益，至少为完全知晓实际交易者价值实现的全能代理的一半。
原文摘要 · Abstract (English)
We study a contextual version of the repeated brokerage problem. In each interaction, two traders with private valuations for an item seek to buy or sell based on the learner's-a broker-proposed price, which is informed by some contextual information. The broker's goal is to maximize the traders' net utility-also known as the gain from trade-by minimizing regret compared to an oracle with perfect knowledge of traders' valuation distributions. We assume that traders' valuations are zero-mean perturbations of the unknown item's current market value-which can change arbitrarily from one interaction to the next-and that similar contexts will correspond to similar market prices. We analyze two feedback settings: full-feedback, where after each interaction the traders' valuations are revealed to the broker, and limited-feedback, where only transaction attempts are revealed. For both feedback types, we propose algorithms achieving tight regret bounds. We further strengthen our performance guarantees by providing a tight 1/2-approximation result showing that the oracle that knows the traders' valuation distributions achieves at least 1/2 of the gain from trade of the omniscient oracle that knows in advance the actual realized traders' valuations.
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