多边贸易中利润最大化的支持依赖遗憾界
Support-Dependent Regret Rates for Profit Maximization in Multilateral Trade
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中文总结 AI 辅助
针对多边贸易中的在线利润最大化问题，提出一种归一化缩放算法，实现支持依赖遗憾界 $\widetilde O(\sqrt{K^dT})$，将一维动态定价的最优保证扩展到多维设置。
中文摘要 AI 辅助
我们研究多边贸易中的在线利润最大化问题，该设置同时推广了动态定价和双边贸易。在每一轮中，中介向买家发布价格并向卖家提供支付；只有当所有代理都接受时，交易才会发生。我们考虑来自未知联合分布的估值，允许代理之间存在任意相关性，并假设每个代理的边际估值分布具有未知支持集，其大小至多为 $K$。对于常数维度 $d$，我们设计了一种遗憾界为 $\widetilde O(\sqrt{K^dT})$ 的算法。这将一维动态定价的最优支持依赖保证扩展到了多边贸易的多维设置。我们方法的核心是一种归一化缩放过程，它适应局部交易概率，避免了标准缩放可能导致的近乎平坦区域的过度细化。
英文摘要
We study online profit maximization in multilateral trade, a setting that generalizes both dynamic pricing and bilateral trade. At each round, an intermediary posts prices to buyers and offers payments to sellers; trade occurs only if every agent accepts. We consider valuations drawn from an unknown joint distribution, allowing arbitrary correlation across agents, under the assumption that each agent's marginal valuation distribution has unknown support of size at most $K$. For constant dimension $d$, we design an algorithm with regret $\widetilde O(\sqrt{K^dT})$. This extends optimal support-dependent guarantees for one-dimensional dynamic pricing to the multidimensional setting of multilateral trade. At the core of our approach is a normalized zooming procedure that adapts to the local probability of trade, avoiding the excessive refinement of nearly flat regions that can arise with standard zooming.
发表机构
- Politecnico di Milano（米兰理工大学）
机构由 AI 辅助整理，请以论文原文为准。
