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对于受约束的马尔科夫决策过程的渐变感知搜索算法
一个新的渐变感知搜索 (GAS) 算法通过利用一块式线性凸 (PWLC) 目标函数,有效地解决受约束的马尔科夫决策过程 (CMDP). 这种方法可以在没有超参数调整的情况下快速趋同到最佳解决方案.
科学领域:
- 运营研究 运营研究
- 人工智能的人工智能
- 控制理论 控制理论
背景情况:
- 约束的马尔科夫决策过程 (CMDP) 通常使用凸线性编程 (LP) 来解决.
- 现有的方法可能需要超参数调整,并且可能对初始条件敏感.
研究的目的:
- 开发一种新的,高效的算法来解决有限的CMDPs.
- 分析CMDP中双线性程序的属性.
- 将拟议的算法与现有的基准方法进行比较.
主要方法:
- 在有限的CMDP中证明双线程序的目标函数的断片线性凸 (PWLC) 结构.
- 开发一个两级梯度感知搜索 (GAS) 算法,利用PWLC属性.
- 将GAS算法应用于两个受约束的随机控制问题.
主要成果:
- 有限CMDP的双目标函数被证明是PWLC与拉格朗日乘数相关.
- 拟议的GAS算法很快就会趋于CMDP的最佳解决方案.
- 气体表现出稳健性,对拉格朗奇乘数的初始化不敏感,不需要超参数调整.
结论:
- GAS算法为解决有限的CMDPs提供了一个可证明的最佳和有效的方法.
- 双重问题的PWLC结构是算法的性能关键.
- 与二进制搜索和基于LP的方法等传统方法相比,GAS提供了显著的改进.
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