This article addresses the challenge of parameter calibration in stochastic models where the likelihood function is not analytically available. We propose a gradient-based simulated parameter estimation framework, leveraging a multi-time scale algorithm that tackles the issue of ratio bias in both maximum likelihood estimation and posterior density estimation problems. Additionally, we introduce a nested simulation optimization structure, providing theoretical analyses including strong convergence, asymptotic normality, convergence rate, and budget allocation strategies for the proposed algorithm. The framework is further extended to neural network training, offering a novel perspective on stochastic approximation in machine learning. Numerical experiments show that our algorithm can improve the estimation accuracy and save computational costs.

翻译：本文针对随机模型中似然函数无法解析获取的参数标定难题，提出一种基于梯度的模拟参数估计框架。该框架采用多时间尺度算法，有效解决了最大似然估计与后验密度估计中的比率偏差问题。此外，我们引入嵌套仿真优化结构，为所提算法提供了包括强收敛性、渐近正态性、收敛速率及预算分配策略在内的理论分析。该框架进一步扩展至神经网络训练领域，为机器学习中的随机逼近方法提供了新视角。数值实验表明，所提算法能有效提升估计精度并节约计算成本。