双城记：离线动态定价中的悲观主义与机会主义
A Tale of Two Cities: Pessimism and Opportunism in Offline Dynamic Pricing
AI总结：
针对历史数据未覆盖部分价格空间（包括最优价格）的离线动态定价问题，提出利用需求单调性的非参数部分识别框架，并设计了悲观策略（最大化最坏情况收入）和机会策略（最小化最坏情况遗憾），在无覆盖环境中优于标准离线强化学习方法。
摘要：
我们研究离线动态定价，当历史数据对价格空间的覆盖不完整时，一些候选价格（包括最优价格）可能完全未被观测到。这种设置在现实中很常见，在动态环境中尤其困难。现有的离线强化学习方法通常依赖于完全或部分覆盖，因此在这种设置下表现不佳。我们开发了一个用于离线动态定价的非参数部分识别框架，利用需求在价格上的单调性来界定未观测价格的价值。在该框架内，我们制定了两种动态决策规则：一种最大化最坏情况收入的悲观策略，和一种最小化最坏情况遗憾的机会策略。这些规则针对顺序无覆盖环境量身定制，并非现有悲观离线强化学习或静态机会主义方法的直接扩展。我们为两种策略建立了有限样本遗憾界，当最优价格被覆盖时恢复了标准速率，并量化了未覆盖时的额外成本。我们还开发了高效算法，并通过模拟和机票应用表明，我们的方法在无覆盖设置中优于标准离线强化学习基线。从管理角度看，该框架提供了从公司风险态度到定价策略的实用映射：寻求收入稳定和下行保护的公司应偏好悲观策略，而愿意承担适度风险以从未充分探索的价格中获取潜在收益的公司应偏好机会策略。
英文摘要：
We study offline dynamic pricing when historical data provide incomplete coverage of the price space such that some candidate prices, including the optimal one, may be entirely unobserved. This setting is common in practice and is especially difficult in dynamic environments. Existing offline reinforcement learning methods typically rely on full or partial coverage and can therefore perform poorly in such settings. We develop a nonparametric partial identification framework for offline dynamic pricing that exploits the monotonicity of demand in price to bound the value of unobserved prices. Within this framework, we formulate two dynamic decision rules: a pessimistic policy that maximizes worst-case revenue and an opportunistic policy that minimizes worst-case regret. These rules are tailored to a sequential no-coverage environment and are not direct extensions of existing pessimistic offline RL or static opportunistic approaches. We establish finite-sample regret bounds for both policies, recovering the standard rate when the optimal price is covered and quantifying the additional cost when it is not. We also develop efficient algorithms and show, through simulations and an airline ticket application, that our methods outperform standard offline RL baselines in no-coverage settings. Managerially, the framework provides a practical mapping from a firm's risk posture to its pricing policy: firms seeking revenue stability and downside protection should prefer the pessimistic policy, whereas firms willing to bear measured risk for potential gains from underexplored prices should prefer the opportunistic policy.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
