Abstract: This work introduces a unified slot machine framework for global optimization, transforming the search for global optimizers into the formulation of an optimal bandit strategy over infinite policy sets. Inspired by AlphaGo's success with Monte Carlo Tree Search, we develop the Strategic Monte Carlo Optimization (SMCO) algorithm, which extends the exploration space by employing tree search methods. SMCO generates points coordinate-wise from paired distributions, facilitating parallel implementation for high-dimensional continuous functions. Unlike gradient descent ascent (GDA), which follows a single-directional path and depends on initial points and step sizes, SMCO takes a two-sided sampling approach, ensuring robustness to these parameters. We establish convergence to global optimizers almost surely and prove a strategic law of large numbers for nonlinear expectations. Numerical results demonstrate that SMCO outperforms GDA, particle swarm optimization, and simulated annealing in both speed and accuracy.

Biography: 严晓东，西安交通大学数学与统计学院教授，博士生导师，入选国家级青年人才项目和校内青拔A类支持计划，滴滴盖亚学者，研究成果发表在统计学著名期刊JRSSB, AOS, JASA和计量经济著名期刊JOE以及人工智能顶级会议AAAI,AISTAT等。