Simulation Optimization with Risk Measures

2025年1月15日（周三）10:00 – 12:00

信息管理与工程学院308会议室

Meichen Song (宋美晨) is a Ph.D. candidate under the supervision of Professor Jiaqiao Hu in the Department of Applied Mathematics and Statistics at Stony Brook University. She received a B.S. degree in Mathematics from Southeast University. Her dissertation focuses on developing and analyzing algorithms for simulation optimization with risk measures and Nash Equilibrium refinement in multi-agent reinforcement learning.

Simulation Optimization with Risk Measures

Complex systems in science and engineering are often highly nonlinear and subject to significant random uncertainties, necessitating the use of simulation models for performance evaluation. In high-stakes fields such as insurance, engineering safety, finance, and healthcare, managing risks from extreme events is critical for understanding worst-case scenarios. Our research focuses on developing simulation-based optimization algorithms for stochastic black-box systems to quantify and optimize unknown risk functions, particularly value-at-risk (VaR) and conditional value-at-risk (CVaR). We proposed two iterative multi-timescale local search algorithms that operate on different timescales to simultaneously estimate risk measure values, gradients of the risk function, and optimal system parameters. Rather than relying on order statistics to approximate VaR, we proposed a stochastic approximation recursion to iteratively approximate VaR values. This method eliminates estimation bias and noise by averaging all historical data collected during iterations. Notably, this approach requires only a single simulation observation per iteration to approximate VaR values. Furthermore, the algorithms employ simultaneous-perturbation-based gradient estimators that use only three observations per iteration to estimate and optimize risk measures, irrespective of the problem’s dimensionality. This efficiency makes the algorithms suitable for high-dimensional problems. Under appropriate conditions, we demonstrate the almost sure convergence of both algorithms. Additionally, for the class of strongly convex functions, we further establish their finite-time convergence rates through a novel fixed-point argument. Simulation experiments confirm the effectiveness of the algorithms across a variety of test problems, including high-dimensional systems with heavy-tailed distributed noise and practical applications such as queuing systems.