Uniform Exponential Convergence of SAA with AMIS and Asymptotics of Its Optimal Value
研究了自适应多重重要性抽样下样本均值逼近的一致指数收敛性,并借助泛函中心极限定理和Delta定理证明其最优值的渐近分布,对随机优化与蒙特卡洛方法研究者有参考价值。
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.