Two-Layer Smooth Approximation for Solving Probabilistic Constrained Programs

Probabilistic constrained program is essential for safety-critical decision-making problems. It can also be extended to give robust uncertainty quantification, robust classification with noisy labels, and many other applications in machine learning or artificial intelligence. However, the existing methods for solving probabilistic constrained program suffers from the issues of giving too conservative solutions and having low computational efficiency, which limits the application of probabilistic constrained program. The two-layer smooth approximation method presented in this paper overcame the above issues. With a significant decrease in computation burden, the proposed method can be applied in various applications, including robust decision-making and classification.