Uniform Exponential Convergence of SAA with AMIS and Asymptotics of Its Optimal Value
Abstract
Abstract. We discuss in this paper uniform exponential convergence of sample average approximation (SAA) with adaptive multiple importance sampling (AMIS) and asymptotics of its optimal value. Using a concentration inequality for bounded martingale differences, we obtain a new exponential convergence rate. To study the asymptotics, we first derive an important functional central limit theorem for martingale difference sequences. Subsequently, exploiting this result with the Delta theorem, we prove the asymptotics of optimal values for SAA with AMIS.
Fields of Study & Subjects
Fault Detection and Control Systems
Fuzzy Logic and Control Systems
Neural Networks and Applications
Publication details
- Journal / source
- SIAM Journal on Optimization
- Volume
- 36
- Issue
- 3
- Pages
- 1326–1355
- Publication date
- 7 July 2026
- Language
- EN