用上下文生成少量高质量决策场景,提升不确定环境下的规划效率
Contextual Scenario Generation for Two-Stage Stochastic Programming
- 根据上下文信息学习生成少数代表性场景
- 两种方法分别从分布逼近和决策质量优化角度提升效果
- 适用于需快速决策的供应链、能源调度等场景
两阶段随机规划(2SP)广泛用于不确定性环境下的决策,但其实际应用常受限于需大量场景来近似不确定结果的条件分布。本文研究上下文场景生成:给定上下文信息,学习生成一组用户指定数量的代理场景,将其输入2SP后可获得高质量决策。现有方法或忽略上下文信息,或在此场景下计算成本过高。本文提出上下文场景生成(CSG),学习从上下文到代理场景集的映射。开发了两种互补方法:(i) 分布式方法,通过最小化核距离逼近条件分布;(ii) 任务导向方法,通过微分学习的2SP目标代理来优化决策质量。两种方法均只需重复求解底层子问题及基于生成场景的2SP。提供有限样本泛化保证,并在多个2SP类别中展示强性能。
原文摘要 · Abstract (English)
Two-stage stochastic programs (2SPs) are widely used for decision-making under uncertainty, but their practical deployment is often limited by the large number of scenarios needed to approximate the conditional distribution of uncertain outcomes. We study contextual scenario generation: given contextual information, learn to produce a small, user-specified set of surrogate scenarios that, when used as input into the 2SP, lead to high-quality 2SP decisions. Existing scenario generation methods either ignore contextual information or are computationally burdensome in this setting. We propose contextual scenario generation (CSG), which learns a mapping from context to a set of surrogate scenarios. We develop two complementary methodologies: (i) a distributional approach that learns a mapping from context to scenarios by minimizing a kernel-based distance to the conditional distribution, and (ii) a task-based approach that selects the mapping to optimize decision quality via differentiating through a learned surrogate of the downstream 2SP objective. Both approaches are broadly applicable and require only repeated solution of the underlying subproblems and 2SPs defined on the generated scenarios. We provide finite-sample generalization guarantees and demonstrate strong empirical performance across multiple 2SP classes.
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