提出一种新框架，让决策在预测不断更新时仍能保持最优竞争力。
A Minimax-MDP Framework with Future-imposed Conditions for Learning-augmented Problems
- 构建最小最大马尔可夫决策模型，结合对手环境与可控状态
- 设计未来约束条件，实现可闭式求解的稳健策略
- 适用于库存、资源分配等动态预测场景，适合做在线决策
我们研究一类由机器学习算法提供增强预测的序列决策问题。决策者接收未知参数的预测区间，这些区间随时间逐步细化，并希望制定的决策在所有可能的真实值和预测结果下，都与事后最优解具有竞争力。为此，我们提出一种最小最大马尔可夫决策过程（minimax-MDP）框架，系统状态包含对抗性演化的环境状态和由决策者控制的内部状态。引入一组未来施加的约束条件，刻画了minimax-MDP的可行性，并支持设计高效、常具闭式解的鲁棒竞争策略。通过三个应用实例验证：多期库存订货与不断精炼的需求预测、不确定效用函数下的资源分配，以及带时变订货成本的多阶段扩展库存问题。结果表明该方法为预测不确定性下的稳健在线决策提供了可计算且通用的解决方案。
原文摘要 · Abstract (English)
We study a class of sequential decision-making problems with augmented predictions, potentially provided by a machine learning algorithm. In this setting, the decision-maker receives prediction intervals for unknown parameters that become progressively refined over time, and seeks decisions that are competitive with the hindsight optimal under all possible realizations of both parameters and predictions. We propose a minimax Markov Decision Process (minimax-MDP) framework, where the system state consists of an adversarially evolving environment state and an internal state controlled by the decision-maker. We introduce a set of future-imposed conditions that characterize the feasibility of minimax-MDPs and enable the design of efficient, often closed-form, robustly competitive policies. We illustrate the framework through three applications: multi-period inventory ordering with refining demand predictions, resource allocation with uncertain utility functions, and a multi-phase extension of the minimax-MDP applied to the inventory problem with time-varying ordering costs. Our results provide a tractable and versatile approach to robust online decision-making under predictive uncertainty.
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