Riemannian Constrained Policy Optimization via Geometric Stability Certificates
Riemannian Constrained Policy Optimization via Geometric Stability Certificates
复制标题
通过几何稳定性证书的黎曼约束策略优化
DOI：
10.1109/cdc51059.2022.9992877
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
Mesbahi, Mehran
中科院分区：
文献类型：
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作者：
Talebi, Shahriar;Mesbahi, Mehran
在本文中，我们考虑的政策优化的黎曼子流形的稳定控制器所产生的约束线性二次型调节器（LQR），包括输出反馈和结构综合。在这个方向上，我们提供了一个黎曼牛顿型算法，享有局部收敛保证，并利用固有的几何问题。该算法不依赖于指数映射或全局收缩，而是围绕开发的稳定性证书和约束结构，利用合成问题的内在几何结构。然后，我们通过数值例子展示了所提出的算法的实用性。
In this paper, we consider policy optimization over the Riemannian submanifolds of stabilizing controllers arising from constrained Linear Quadratic Regulators (LQR), including output feedback and structured synthesis. In this direction, we provide a Riemannian Newton-type algorithm that enjoys local convergence guarantees and exploits the inherent geometry of the problem. Instead of relying on the exponential mapping or a global retraction, the proposed algorithm revolves around the developed stability certificate and the constraint structure, utilizing the intrinsic geometry of the synthesis problem. We then showcase the utility of the proposed algorithm through numerical examples.