论文标题
决策问题的参数化凸通用近似值
Parameterized Convex Universal Approximators for Decision-Making Problems
论文作者
论文摘要
为一般决策问题提出了参数化的最大疗法（PMA）和参数化的对数-SUM-EXP（PLSE）网络。所提出的近似值通过考虑条件和决策变量的函数参数，并替换具有连续功能的条件与条件变量的函数，从而概括了现有的凸近似值，即Max-Affine（MA）和Log-Sum-Exp（LSE）网络。证明了PMA和PLSE的通用近似定理，这意味着PMA和PLSE是具有形状的具有参数化凸连续函数的通用通用近似值。提供了将深层神经网络纳入PMA和PLSE网络中的实用指南。进行数值模拟以证明所提出的近似器的性能。模拟结果支持，在最小化和最佳价值误差方面，PLSE的表现优于其他现有近似值，并且对于高维情况而言，可扩展有效的计算。
Parameterized max-affine (PMA) and parameterized log-sum-exp (PLSE) networks are proposed for general decision-making problems. The proposed approximators generalize existing convex approximators, namely, max-affine (MA) and log-sum-exp (LSE) networks, by considering function arguments of condition and decision variables and replacing the network parameters of MA and LSE networks with continuous functions with respect to the condition variable. The universal approximation theorem of PMA and PLSE is proven, which implies that PMA and PLSE are shape-preserving universal approximators for parameterized convex continuous functions. Practical guidelines for incorporating deep neural networks within PMA and PLSE networks are provided. A numerical simulation is performed to demonstrate the performance of the proposed approximators. The simulation results support that PLSE outperforms other existing approximators in terms of minimizer and optimal value errors with scalable and efficient computation for high-dimensional cases.
