论文标题
双层梯度下降算法的输入到州的稳定性
Input-to-State Stability of a Bilevel Proximal Gradient Descent Algorithm
论文作者
论文摘要
本文研究了不精确的迭代溶液方案的收敛特性，这些方案用于二聚体优化问题。在控制吸引设计优化中出现了双光线优化问题，其中系统设计参数在外循环中进行了优化，并且在内部循环中优化了离散的时间控制轨迹，但在包括机器学习在内的其他域中也会出现。在本文中，提出了近端梯度算法的互连，以从控制理论的角度来分析控制感知设计优化和鲁棒性的内部环路优化问题。通过采用输入到国家稳定性参数，可以得出条件，以确保将互连方案收敛到一类双层优化问题的最佳解决方案。
This paper studies convergence properties of inexact iterative solution schemes for bilevel optimization problems. Bilevel optimization problems emerge in control-aware design optimization, where the system design parameters are optimized in the outer loop and a discrete-time control trajectory is optimized in the inner loop, but also arise in other domains including machine learning. In the paper an interconnection of proximal gradient algorithms is proposed to solve the inner loop and outer loop optimization problems in the setting of control-aware design optimization and robustness is analyzed from a control-theoretic perspective. By employing input-to-state stability arguments, conditions are derived that ensure convergence of the interconnected scheme to the optimal solution for a class of the bilevel optimization problem.
