提出新型多阶段优化框架，高效解决不确定性下的决策问题。
Multistage Conditional Compositional Optimization
- 采用嵌套条件期望与非线性代价函数的组合优化思路
- 新方法使场景复杂度随精度呈多项式增长，克服指数爆炸问题
- 适合动态风险控制、强化学习等需要多阶段决策的场景
我们提出多阶段条件组合优化（MCCO），一种在不确定性下进行决策的新范式，融合了多阶段随机规划与条件随机优化的特点。MCCO旨在最小化嵌套的条件期望与非线性代价函数。该框架具有广泛的应用，例如最优停止、线性二次调节器问题、分布鲁棒上下文老虎机，以及涉及动态风险测度的问题。传统的嵌套采样方法在处理MCCO时面临典型的维度灾难，即场景复杂度随嵌套层数呈指数增长。为此，我们开发了新的多级蒙特卡洛技术，使得场景复杂度仅随所需精度呈多项式增长，显著提升了计算效率。
原文摘要 · Abstract (English)
We introduce Multistage Conditional Compositional Optimization (MCCO) as a new paradigm for decision-making under uncertainty that combines aspects of multistage stochastic programming and conditional stochastic optimization. MCCO minimizes a nest of conditional expectations and nonlinear cost functions. It has numerous applications and arises, for example, in optimal stopping, linear-quadratic regulator problems, distributionally robust contextual bandits, as well as in problems involving dynamic risk measures. The naïve nested sampling approach for MCCO suffers from the curse of dimensionality familiar from scenario tree-based multistage stochastic programming, that is, its scenario complexity grows exponentially with the number of nests. We develop new multilevel Monte Carlo techniques for MCCO whose scenario complexity grows only polynomially with the desired accuracy.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。